Electric Flux and Gauss's Law and its Applications

Q 1 :

An electric field is given by $(6 \hat{i} + 5 \hat{j} + 3 \hat{k}) N / C .$ The electric flux through a surface area $30 \hat{i}$ $m^{2}$ lying in YZ-plane (in SI unit) is [2024]

180
90
150
60

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(1)

$\vec{E} = (6 \hat{i} + 5 \hat{j} + 3 \hat{k}) N / C$

$\vec{A} = 30 \hat{i}$ $m^{2}$

Electric flux, $ϕ = \vec{E} \cdot \vec{A}$

$ϕ = (6 \hat{i} + 5 \hat{j} + 3 \hat{k}) \cdot (30 \hat{i}) = 180 \frac{N m^{2}}{C}$

Q 2 :

Three infinitely long charged thin sheets are placed as shown in figure. The magnitude of electric field at the point P is $\frac{x σ}{ε_{0}}$ . The value of $x$ is _____ (all quantities are measured in Sl units). [2024]

(2) $\vec{E} = \vec{E_{1}} + \vec{E_{2}} + \vec{E_{3}}$

$= \frac{σ}{2 ε_{0}} (- \hat{i}) + \frac{- 2 σ}{2 ε_{0}} (\hat{i}) + \frac{- σ}{2 ε_{0}} (\hat{i})$

$= - \frac{4 σ}{2 ε_{0}} \hat{i} = \frac{2 σ}{ε_{0}} (- \hat{i})$

Q 3 :

A charge q is placed at the center of one of the surfaces of a cube. The flux linked with the cube is [2024]

$\frac{q}{2 ε_{0}}$
$\frac{q}{4 ε_{0}}$
$\frac{q}{8 ε_{0}}$
$zero$

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(1)

$ϕ_{total} = \frac{q_{en}}{ε_{0}}$

Let us enclose the charge with an identical cube as shown,

$Total flux, 2 ϕ = \frac{q}{ε_{0}} \Rightarrow ϕ = \frac{q}{2 ε_{0}}$

Q 4 :

Five charges +q, +5q, −2q, +3q and −4q are situated as shown in the figure. The electric flux due to this configuration through the surface S is [2024]

$\frac{5 q}{ε_{0}}$
$\frac{4 q}{ε_{0}}$
$\frac{3 q}{ε_{0}}$
$\frac{q}{ε_{0}}$

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(2)

As per Gauss' theorem,

$ϕ = \frac{q_{in}}{ε_{0}} = \frac{q + (- 2 q) + 5 q}{ε_{0}} = \frac{4 q}{ε_{0}}$

Q 5 :

Two charges of 5Q and −2Q are situated at the points (3a,0) and (−5a,0) respectively. The electric flux through a sphere of radius 4a having center at origin is [2024]

$\frac{2 Q}{ε_{0}}$
$\frac{5 Q}{ε_{0}}$
$\frac{7 Q}{ε_{0}}$
$\frac{3 Q}{ε_{0}}$

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(2)

If we draw the sphere, the charge -2Q will be outside of sphere and 5Q charge is inside the spherical region

The flux through sphere $\frac{5 Q}{ε_{0}}$

Q 6 :

$C_{1}$ and $C_{2}$ are two hollow concentric cubes enclosing charges 2Q and 3Q respectively as shown in the figure. The ratio of electric flux passing through $C_{1}$ and $C_{2}$ is [2024]

2 : 5
5 : 2
2 : 3
3 : 2

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(1)

Flux through $C_{1}$ , $ϕ_{1} = \frac{q_{in}}{ε_{0}} = \frac{2 Q}{ε_{0}}$

Flux through $C_{2}$ , $ϕ_{2} = \frac{q_{in}}{ε_{0}} = \frac{2 Q + 3 Q}{ε_{0}} = \frac{5 Q}{ε_{0}}$

$\frac{C_{1}}{C_{2}} = \frac{ϕ_{1}}{ϕ_{2}} = \frac{2 Q / ε_{0}}{5 Q / ε_{0}} = \frac{2}{5}$

Q 7 :

An infinite plane sheet of charge having uniform surface charge density $+ σ_{s}$ $C / m^{2}$ is placed on the $x - y$ plane. Another infinitely long line charge having uniform linear charge density $+ λ_{e}$ $C / m$ is placed at $z = 4$ m plane and parallel to the y-axis. If the magnitude values $∣ σ_{s} ∣ = 2 ∣ λ_{e} ∣$ then at point $(0, 0, 2),$ the ratio of magnitudes of electric field values due to sheet charge to that of line charge is $π \sqrt{n} : 1$ . The value of $n$ is ______ . [2024]

(16)

${\vec{E}}_{sheet} = \frac{σ_{s}}{2 ε_{0}} \hat{k} = \frac{λ_{e}}{ε_{0}} \hat{k}$

${\vec{E}}_{wire} = \frac{2 k λ_{e}}{r} (- \hat{k}) = \frac{2 k λ_{e}}{2} (- \hat{k}) = k λ (- \hat{k})$

$\frac{| {\vec{E}}_{sheet} |}{| {\vec{E}}_{wire} |} = \frac{λ_{e}}{ε_{0}} \times \frac{1}{k λ_{e}} = \frac{1}{ε_{0} k} = \frac{1}{ε_{0} \times \frac{1}{4 π ε_{0}}} = 4 π$

$\Rightarrow 4 π = π \sqrt{n} \Rightarrow n = 16$

Q 8 :

An electric field, $\vec{E} = \frac{2 \hat{i} + 6 \hat{j} + 8 \hat{k}}{\sqrt{6}}$ passes through the surface of $4 m^{2}$ area having unit vector $\hat{n} = (\frac{2 \hat{i} + \hat{j} + \hat{k}}{\sqrt{6}}) .$ The electric flux for that surface is ____ Vm. [2024]

(12)

$ϕ = \vec{E} \cdot \vec{A} = (\frac{2 \hat{i} + 6 \hat{j} + 8 \hat{k}}{\sqrt{6}}) \cdot 4 (\frac{2 \hat{i} + \hat{j} + \hat{k}}{\sqrt{6}})$

$ϕ = \frac{4}{6} \times (4 + 6 + 8) = 12 Vm$

Q 9 :

An electric field $\vec{E} = (2 x \hat{i}) N C^{- 1}$ exists in space. A cube of side 2 m is placed in the space as per figure given below. The electric flux through the cube is _____ ${Nm}^{2} / C .$ [2024]

(16)

Given $\vec{E} = (2 x \hat{i}) N/C$

$ϕ = \vec{E} \cdot \vec{A}$

$ϕ_{in} = - 4 \times 4 = - 16 {Nm}^{2} / C$

$ϕ_{out} = 8 \times 4 = 32 {Nm}^{2} / C$

$ϕ_{net} = ϕ_{in} + ϕ_{out} = - 16 + 32 = 16 {Nm}^{2} / C$

Q 10 :

A line charge of length $\frac{' a'}{2}$ is kept at the center of an edge BC of a cube ABCDEFGH having edge length 'a' as shown in the figure. If the density of line charge is $λ$ C per unit length, then the total electric flux through all the faces of the cube will be ______ (Take, $ε_{0}$ as the free space permittivity) [2025]

$\frac{λ a}{8 ε_{0}}$
$\frac{λ a}{16 ε_{0}}$
$\frac{λ a}{2 ε_{0}}$
$\frac{λ a}{4 ε_{0}}$

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(1)

Charge of the line charge $= \frac{a λ}{2}$

Portion of wire inside cube $= \frac{1}{4}$

Total charge inside the cube, $q_{en} = \frac{1}{4} (\frac{a λ}{2}) = \frac{λ a}{8}$

$∴ ϕ = \frac{q_{en}}{ε_{0}} = \frac{λ a}{8 ε_{0}}$

Q 11 :

Match List I with List II

List I List II

A. Electric field inside (distance r > 0 from center) of a uniformly charged spherical shell with surface charge density $σ$ , and radius R. I. $σ / ε_{0}$

B. Electric field at distance r > 0 from a uniformly charged infinite plane sheet with surface charge density $σ$ . II. $σ / 2 ε_{0}$

C. Electric field outside (distance r > 0 from center) of a uniformly charged spherical shell with surface charge density $σ$ , and radius R. III. 0

D. Electric field between 2 oppositely charged infinite plane parallel sheets with uniform surface charge density $σ$ . IV. $σ / ε_{0} r^{2}$

Choose the correct answer from the options given below: [2025]

(A)-(IV), (B)-(I), (C)-(III), (D)-(II)
(A)-(IV), (B)-(II), (C)-(III), (D)-(I)
(A)-(II), (B)-(I), (C)-(IV), (D)-(III)
(A)-(III), (B)-(II), (C)-(IV), (D)-(I)

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(none)

Inside uniformly charged spherical shell, E = 0

$∴ A \to III$

For uniformly charged infinite plate

$E = \frac{σ}{2 ε_{0}}$

$B \to II$

Outside of spherical shell

$E = \frac{Q}{4 π ε_{0} r^{2}} = \frac{σ R^{2}}{ε_{0} r^{2}}$

None of the option is matching for C.

Between two plates $E = \frac{σ}{ε_{0}}$

$D \to I$

None of the option is correct.

Q 12 :

A point charge causes an electric flux of $- 2 \times 10^{4} {Nm}^{2} C^{- 1}$ to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is: (Given $ε_{0} = 8.85 \times 10^{- 12} C^{2} N^{- 1} m^{- 2}$ ) [2025]

$- 17.7 \times 10^{- 8} C$
$- 15.7 \times 10^{- 8} C$
$17.7 \times 10^{- 8} C$
$15.7 \times 10^{- 8} C$

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(1)

$ϕ = - 2 \times 10^{4} \frac{{Nm}^{2}}{C}$

$ϕ = \frac{q}{ε_{0}}$

$\Rightarrow q = ε_{0} ϕ = (8.85 \times 10^{- 12}) \times (- 2 \times 10^{4})$

$q = - 17.7 \times 10^{- 8} C$

Q 13 :

Consider two infinitely large plane parallel conducting plates as shown below. The plates are uniformly charged with a surface charge density $+ σ$ and $- 2 σ$ . The force experienced by a point charge $+ q$ placed at the midpoint between two plates will be: [2025]

$\frac{σ q}{4 ε_{0}}$
$\frac{3 σ q}{2 ε_{0}}$
$\frac{3 σ q}{4 ε_{0}}$
$\frac{σ q}{2 ε_{0}}$

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(2)

Final charge distribution on different surfaces,

Electric field between the plates,

$E = E_{1} + E_{2} = \frac{(\frac{3}{2} σ)}{2 ε_{0}} + \frac{(\frac{3}{2} σ)}{2 ε_{0}} = \frac{3 σ}{2 ε_{0}}$

$\Rightarrow F = E q = \frac{3 σ q}{2 ε_{0}}$

Q 14 :

Two infinite identical charged sheets and a charged spherical body of charge density ' $ρ$ ' are arranged as shown in figure. Then the correct relation between the electrical fields at A, B, C and D points is: [2025]

${\vec{E}}_{A} = {\vec{E}}_{B}; {\vec{E}}_{C} = {\vec{E}}_{D}$
${\vec{E}}_{A} > {\vec{E}}_{B}; {\vec{E}}_{C} = {\vec{E}}_{D}$
${\vec{E}}_{C} \neq {\vec{E}}_{D}; {\vec{E}}_{A} > {\vec{E}}_{B}$
$| {\vec{E}}_{A} | = | {\vec{E}}_{B} |; {\vec{E}}_{C} > {\vec{E}}_{D}$

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(3)

At points A and B sum of field due to plates is zero.

A is closer to the body so ${\vec{E}}_{A} > {\vec{E}}_{B}$ .

D and C are not symmetric w.r.t. body so $E_{C} \neq E_{D}$

Q 15 :

Two small spherical balls of mass 10 g each with charges $- 2 μ C$ and $2 μ C$ , are attached to two ends of very light rigid rod of length 20 cm. The arrangement is now placed near an infinite non-conducting charge sheet with uniform charge density of 100 $μ C / m^{2}$ such that length of rod makes an angle of 30° with electric field generated by charge sheet. Net torque acting on the rod is: (Take $ε_{0} : 8.85 \times 10^{- 12} C^{2} / {Nm}^{2}$ ) [2025]

112 Nm
1.12 Nm
2.24 Nm
11.2 Nm

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(2)

$E = \frac{σ}{2 ε_{0}} = \frac{100 \times 10^{- 6}}{2 \times 8.85 \times 10^{- 12}} N / C$

$τ = P E \sin θ = q d E \sin θ$

$= 2 \times 10^{- 6} \times 0.2 \times \frac{100 \times 10^{- 6}}{2 \times 8.85 \times 10^{- 12}} \times \frac{1}{2}$

$\Rightarrow τ = 1.12 Nm$

Q 16 :

An infinitely long wire has uniform linear charge density $λ = 2 nC / m$ . The net flux through a Gaussian cube of side length $\sqrt{3} cm$ , if the wire passes through any two corners of the cube, that are maximally displaced from each other would be $x {Nm}^{2} C^{- 1}$ , where x is: [Neglect any edge effects and use $\frac{1}{4 π ε_{0}} = 9 \times 10^{9} SI units$ ] [2025]

0.72 $π$
4.44 $π$
6.48 $π$
2.16 $π$

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(4)

$ϕ = \frac{q_{enclosed}}{ε_{0}}$

$l = \sqrt{3} a = 3 cm$

$q_{enclosed} = λ l$

$\Rightarrow ϕ = \frac{λ l}{ε_{0}}$

$= 2 \times 10^{- 9} \times 3 \times 10^{- 2} \times 4 π \times 9 \times 10^{9}$

$= 2.16 π$

Q 17 :

A square loop of sides a = 1 m is held normally in front of a point charge q = 1 C. The flux of the electric field through the shaded region is $\frac{5}{p} \times \frac{1}{ε_{0}} \frac{{Nm}^{2}}{C}$ , where the value of p is __________. [2025]

(48)

Total flux through square $= \frac{q}{ε_{0}} (\frac{1}{6})$

Lets divide square in 8 equal parts.

Flux is same for each part.

$∴$ Flux through shaded portion is $\frac{5}{8}$ (Total flux)

$= \frac{5}{8} \times \frac{q}{ε_{0}} \frac{1}{6} = \frac{5}{48} \frac{1}{ε_{0}}$

Q 18 :

The electric field in a region is given by $\vec{E} = (2 \hat{i} + 4 \hat{j} + 6 \hat{k}) \times 10^{3} N / C$ . The flux of the field through a rectangular surface parallel to x – z plane is 6.0 ${Nm}^{2} C^{- 1}$ . The area of the surface is __________ ${cm}^{2}$ . [2025]

(15)

$ϕ = \vec{E} \cdot \vec{A} = (2 \hat{i} + 4 \hat{j} + 6 \hat{k}) \times 10^{3} \cdot A \hat{j}$

$6 = 4 \times 10^{3} A$

$A = 1.5 \times 10^{- 3} m^{2} = 15 {cm}^{2}$

Q 19 :

Let $σ$ be the uniform surface charge density of two infinite thin plane sheets shown in the figure. Then the electric fields in three different regions $E_{I}$ , $E_{I I}$ and $E_{I I I}$ is [2023]

${\vec{E}}_{I} = \frac{2 σ}{ε_{0}} \hat{n}, {\vec{E}}_{I I} = 0, {\vec{E}}_{I I I} = \frac{2 σ}{ε_{0}} \hat{n}$
${\vec{E}}_{I} = 0, {\vec{E}}_{I I} = \frac{σ}{ε_{0}} \hat{n}, {\vec{E}}_{I I I} = 0$
${\vec{E}}_{I} = \frac{σ}{2 ε_{0}} \hat{n}, {\vec{E}}_{I I} = 0, {\vec{E}}_{I I I} = \frac{σ}{2 ε_{0}} \hat{n}$
${\vec{E}}_{I} = - \frac{σ}{ε_{0}} \hat{n}, {\vec{E}}_{I I} = 0, {\vec{E}}_{I I I} = \frac{σ}{ε_{0}} \hat{n}$

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(4)

$Assuming RHS to be \hat{n}$

${\vec{E}}_{I} = \frac{σ}{2 ε_{0}} (- \hat{n}) + \frac{σ}{2 ε_{0}} (- \hat{n}) = - \frac{σ}{ε_{0}} \hat{n}$

${\vec{E}}_{I I} = 0$

${\vec{E}}_{I I I} = \frac{σ}{2 ε_{0}} (\hat{n}) + \frac{σ}{2 ε_{0}} (\hat{n}) = \frac{σ}{ε_{0}} (\hat{n})$

Q 20 :

In a cuboid of dimension $2 L \times 2 L \times L$ , a charge $q$ is placed at the centre of the surface $' S'$ having area $4 L^{2}$ . The flux through the opposite surface to $' S'$ is given by [2023]

$\frac{q}{12 ε_{0}}$
$\frac{q}{3 ε_{0}}$
$\frac{q}{2 ε_{0}}$
$\frac{q}{6 ε_{0}}$

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(4)

$ϕ = \frac{Q / ε_{0}}{6}$

$Flux passing through shaded face = \frac{q}{6 ε_{0}}$

Q 21 :

As shown in the figure, a point charge $Q$ is placed at the centre of the conducting spherical shell of inner radius $a$ and outer radius $b$ . The electric field due to charge $Q$ in three different regions I, II and III is given by:

$(I: r < a, II: a < r < b, III: r > b)$ [2023]

$E_{I} = 0, E_{I I} = 0, E_{I I I} \neq 0$
$E_{I} \neq 0, E_{I I} = 0, E_{I I I} \neq 0$
$E_{I} \neq 0, E_{I I} = 0, E_{I I I} = 0$
$E_{I} = 0, E_{I I} = 0, E_{I I I} = 0$

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(2)

$E_{I} \neq 0 (inside region)$

$E_{I I} = 0 (conducting region)$

$E_{I I I} \neq 0 = \frac{K Q}{r^{2}} (r > b)$

Q 22 :

Given below are two statement: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: If an electric dipole of dipole moment $30 \times 10^{- 5} Cm$ is enclosed by a closed surface, the net flux coming out of the surface will be zero.

Reason R: Electric dipole consists of two equal and opposite charges.

In the light of above statements, choose the correct answer from the options given below: [2023]

Both A and R are true and R is the correct explanation of A
A is true but R is false
Both A and R are true but R is NOT the correct explanation of A
A is false but R is true

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(1)

$\vec{P} = 30 \times 10^{- 5} Cm$

$Using Gauss law$

$ϕ = \frac{Q_{in}}{ε_{0}} and Q_{in} = 0 \Rightarrow ϕ = 0$

Q 23 :

As shown in the figure, a cuboid lies in a region with electric field $\vec{E} = 2 x^{2} \hat{i} - 4 y \hat{j} + 6 \hat{k} N/C.$ The magnitude of charge within the cuboid is $n ε_{0} C$ . The value of $n$ is _______ (if dimensions of cuboid is $1 \times 2 \times 3 m^{3}$ ) [2023]

(12)

$\vec{E} = 2 x^{2} \hat{i} - 4 y \hat{j} + 6 \hat{k}$

$ϕ_{net} = - 8 \times 3 + 2 \times 6 = - 12$

$- 12 = \frac{q}{ε_{0}} \Rightarrow$ $| q |$ $= 12 ε_{0}$

Q 24 :

Expression for an electric field is given by $\vec{E} = 4000 x^{2} \hat{i} V/m .$ The electric flux through the cube of side 20 cm when placed in the electric field (as shown in the figure) is ________ V cm. [2023]

(640)

$Flux = \vec{E} \cdot \vec{A} = 4000 {(0.2)}^{2} \frac{V}{m} \cdot {(0.2)}^{2} m^{2}$

$= 4000 \times 16 \times 10^{- 4} V m = 640 Vcm$

Q 25 :

A cubical volume is bounded by the surfaces $x = 0, x = a, y = 0, y = a, z = 0, z = a$ . The electric field in the region is given by $\vec{E} = E_{0} x \hat{i},$ where $E_{0} = 4 \times 10^{4} {NC}^{- 1} m^{- 1}$ . If $a = 2cm,$ the charge contained in the cubical volume is $Q \times 10^{- 14} C .$ The value of $Q$ is __________. (Take $ε_{0} = 9 \times 10^{- 12} C^{2} {/Nm}^{2}$ ). [2023]

(288)

$\vec{E} = E_{0} x \hat{i}$

$ϕ_{net} = ϕ_{A B C D} = E_{0} a \cdot a^{2}$

$\frac{q_{en}}{ε_{0}} = E_{0} a^{3}$

$\Rightarrow q_{en} = E_{0} ε_{0} a^{3}$

$q_{en} = 4 \times 10^{4} \times 9 \times 10^{- 12} \times 8 \times 10^{- 6} = 288 \times 10^{- 14} C$

$\Rightarrow Q = 288$

Q 26 :

An electron revolves around an infinite cylindrical wire having uniform linear charge density $2 \times 10^{- 8} {Cm}^{- 1}$ in a circular path under the influence of attractive electrostatic field as shown in the figure. The velocity of the electron with which it is revolving is __________ $\times 10^{6} {ms}^{- 1}$ . Given, mass of electron $= 9 \times 10^{- 31} kg$ . [2023]

(8)

$e E = \frac{m v^{2}}{r}$

$e \frac{2 k λ}{r} = \frac{m v^{2}}{r}$

$v = \sqrt{\frac{e \cdot 2 k λ}{m}} = \sqrt{\frac{1.6 \times 10^{- 19} \times 2 \times 9 \times 10^{9} \times 2 \times 10^{- 8}}{9 \times 10^{- 31}}}$

$= 8 \times 10^{6} m/s$

Q 27 :

Two point charges $2 q$ and $q$ are placed at vertex A and centre of face CDEF of the cube as shown in the figure. The electric flux passing through the cube is: [2026]

$\frac{3 q}{2 ε_{0}}$
$\frac{q}{ε_{0}}$
$\frac{3 q}{4 ε_{0}}$
$\frac{3 q}{ε_{0}}$

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(3)

$ϕ = \frac{Q_{in}}{ε_{0}}$

$ϕ = \frac{\frac{q}{4} + \frac{q}{2}}{ε_{0}} = \frac{3 q}{4 ε_{0}}$

Topic Question Set

Q 1 :

An electric field is given by $(6 \hat{i} + 5 \hat{j} + 3 \hat{k}) N / C .$ The electric flux through a surface area $30 \hat{i}$ $m^{2}$ lying in YZ-plane (in SI unit) is [2024]

Q 2 :

Three infinitely long charged thin sheets are placed as shown in figure. The magnitude of electric field at the point P is $\frac{x σ}{ε_{0}}$ . The value of $x$ is _____ (all quantities are measured in Sl units). [2024]

Q 3 :

A charge q is placed at the center of one of the surfaces of a cube. The flux linked with the cube is [2024]

Q 4 :

Five charges +q, +5q, −2q, +3q and −4q are situated as shown in the figure. The electric flux due to this configuration through the surface S is [2024]

Q 5 :

Two charges of 5Q and −2Q are situated at the points (3a,0) and (−5a,0) respectively. The electric flux through a sphere of radius 4a having center at origin is [2024]

Q 6 :

$C_{1}$ and $C_{2}$ are two hollow concentric cubes enclosing charges 2Q and 3Q respectively as shown in the figure. The ratio of electric flux passing through $C_{1}$ and $C_{2}$ is [2024]

Q 8 :

An electric field, $\vec{E} = \frac{2 \hat{i} + 6 \hat{j} + 8 \hat{k}}{\sqrt{6}}$ passes through the surface of $4 m^{2}$ area having unit vector $\hat{n} = (\frac{2 \hat{i} + \hat{j} + \hat{k}}{\sqrt{6}}) .$ The electric flux for that surface is ____ Vm. [2024]

Q 9 :

An electric field $\vec{E} = (2 x \hat{i}) N C^{- 1}$ exists in space. A cube of side 2 m is placed in the space as per figure given below. The electric flux through the cube is _____ ${Nm}^{2} / C .$ [2024]

Q 12 :

A point charge causes an electric flux of $- 2 \times 10^{4} {Nm}^{2} C^{- 1}$ to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is: (Given $ε_{0} = 8.85 \times 10^{- 12} C^{2} N^{- 1} m^{- 2}$ ) [2025]

Q 13 :

Consider two infinitely large plane parallel conducting plates as shown below. The plates are uniformly charged with a surface charge density $+ σ$ and $- 2 σ$ . The force experienced by a point charge $+ q$ placed at the midpoint between two plates will be: [2025]

Q 14 :

Two infinite identical charged sheets and a charged spherical body of charge density ' $ρ$ ' are arranged as shown in figure. Then the correct relation between the electrical fields at A, B, C and D points is: [2025]

Q 17 :

A square loop of sides a = 1 m is held normally in front of a point charge q = 1 C. The flux of the electric field through the shaded region is $\frac{5}{p} \times \frac{1}{ε_{0}} \frac{{Nm}^{2}}{C}$ , where the value of p is __________. [2025]

Q 18 :

The electric field in a region is given by $\vec{E} = (2 \hat{i} + 4 \hat{j} + 6 \hat{k}) \times 10^{3} N / C$ . The flux of the field through a rectangular surface parallel to x – z plane is 6.0 ${Nm}^{2} C^{- 1}$ . The area of the surface is __________ ${cm}^{2}$ . [2025]

Q 19 :

Let $σ$ be the uniform surface charge density of two infinite thin plane sheets shown in the figure. Then the electric fields in three different regions $E_{I}$ , $E_{I I}$ and $E_{I I I}$ is [2023]

Q 20 :

In a cuboid of dimension $2 L \times 2 L \times L$ , a charge $q$ is placed at the centre of the surface $' S'$ having area $4 L^{2}$ . The flux through the opposite surface to $' S'$ is given by [2023]

Q 21 :

As shown in the figure, a point charge $Q$ is placed at the centre of the conducting spherical shell of inner radius $a$ and outer radius $b$ . The electric field due to charge $Q$ in three different regions I, II and III is given by:

$(I: r < a, II: a < r < b, III: r > b)$ [2023]

Q 23 :

As shown in the figure, a cuboid lies in a region with electric field $\vec{E} = 2 x^{2} \hat{i} - 4 y \hat{j} + 6 \hat{k} N/C.$ The magnitude of charge within the cuboid is $n ε_{0} C$ . The value of $n$ is _______ (if dimensions of cuboid is $1 \times 2 \times 3 m^{3}$ ) [2023]

Q 24 :

Expression for an electric field is given by $\vec{E} = 4000 x^{2} \hat{i} V/m .$ The electric flux through the cube of side 20 cm when placed in the electric field (as shown in the figure) is ________ V cm. [2023]

Q 27 :

Two point charges $2 q$ and $q$ are placed at vertex A and centre of face CDEF of the cube as shown in the figure. The electric flux passing through the cube is: [2026]

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	List I		List II
A.	Electric field inside (distance r > 0 from center) of a uniformly charged spherical shell with surface charge density $σ$ , and radius R.	I.	$σ / ε_{0}$
B.	Electric field at distance r > 0 from a uniformly charged infinite plane sheet with surface charge density $σ$ .	II.	$σ / 2 ε_{0}$
C.	Electric field outside (distance r > 0 from center) of a uniformly charged spherical shell with surface charge density $σ$ , and radius R.	III.	0
D.	Electric field between 2 oppositely charged infinite plane parallel sheets with uniform surface charge density $σ$ .	IV.	$σ / ε_{0} r^{2}$

Topic Question Set

Q 1 : An electric field is given by (6i^+5j^+3k^)N/C. The electric flux through a surface area 30i^ m2 lying in YZ-plane (in SI unit) is [2024]

Q 2 : Three infinitely long charged thin sheets are placed as shown in figure. The magnitude of electric field at the point P is xσε0. The value of x is _____ (all quantities are measured in Sl units). [2024]

Q 3 : A charge q is placed at the center of one of the surfaces of a cube. The flux linked with the cube is [2024]

Q 4 : Five charges +q, +5q, −2q, +3q and −4q are situated as shown in the figure. The electric flux due to this configuration through the surface S is [2024]

Q 5 : Two charges of 5Q and −2Q are situated at the points (3a,0) and (−5a,0) respectively. The electric flux through a sphere of radius 4a having center at origin is [2024]

Q 6 : C1 and C2 are two hollow concentric cubes enclosing charges 2Q and 3Q respectively as shown in the figure. The ratio of electric flux passing through C1 and C2 is [2024]

Q 8 : An electric field, E→=2i^+6j^+8k^6 passes through the surface of 4m2 area having unit vector n^=(2i^+j^+k^6). The electric flux for that surface is ____ Vm. [2024]

Q 9 : An electric field E→=(2xi^)NC-1 exists in space. A cube of side 2 m is placed in the space as per figure given below. The electric flux through the cube is _____ Nm2/C. [2024]

Q 12 : A point charge causes an electric flux of –2×104 Nm2C–1 to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is: (Given ε0=8.85×10–12C2N–1m–2) [2025]

Q 13 : Consider two infinitely large plane parallel conducting plates as shown below. The plates are uniformly charged with a surface charge density +σ and –2σ. The force experienced by a point charge +q placed at the midpoint between two plates will be: [2025]

Q 14 : Two infinite identical charged sheets and a charged spherical body of charge density 'ρ' are arranged as shown in figure. Then the correct relation between the electrical fields at A, B, C and D points is: [2025]

Q 17 : A square loop of sides a = 1 m is held normally in front of a point charge q = 1 C. The flux of the electric field through the shaded region is 5p×1ε0Nm2C, where the value of p is __________. [2025]

Q 18 : The electric field in a region is given by E→=(2i^+4j^+6k^)×103 N/C. The flux of the field through a rectangular surface parallel to x – z plane is 6.0 Nm2C–1. The area of the surface is __________cm2 . [2025]

Q 19 : Let σ be the uniform surface charge density of two infinite thin plane sheets shown in the figure. Then the electric fields in three different regions EI, EII and EIII is [2023]

Q 20 : In a cuboid of dimension 2L×2L×L, a charge q is placed at the centre of the surface 'S' having area 4L2. The flux through the opposite surface to 'S' is given by [2023]

Q 21 : As shown in the figure, a point charge Q is placed at the centre of the conducting spherical shell of inner radius a and outer radius b. The electric field due to charge Q in three different regions I, II and III is given by: (I: r<a, II: a<r<b, III: r>b) [2023]

Q 23 : As shown in the figure, a cuboid lies in a region with electric field E→=2x2i^-4yj^+6k^ N/C. The magnitude of charge within the cuboid is nε0 C. The value of n is _______ (if dimensions of cuboid is 1×2×3 m3) [2023]

Q 24 : Expression for an electric field is given by E→=4000x2i^ V/m. The electric flux through the cube of side 20 cm when placed in the electric field (as shown in the figure) is ________ V cm. [2023]

Q 25 : A cubical volume is bounded by the surfaces x=0, x=a, y=0, y=a, z=0, z=a. The electric field in the region is given by E→=E0xi^, where E0=4×104 NC-1m-1. If a=2cm, the charge contained in the cubical volume is Q×10-14 C. The value of Q is __________. (Take ε0=9×10-12 C2/Nm2). [2023]

Q 27 : Two point charges 2q and q are placed at vertex A and centre of face CDEF of the cube as shown in the figure. The electric flux passing through the cube is: [2026]

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Q 1 :

An electric field is given by $(6 \hat{i} + 5 \hat{j} + 3 \hat{k}) N / C .$ The electric flux through a surface area $30 \hat{i}$ $m^{2}$ lying in YZ-plane (in SI unit) is [2024]

Q 2 :

Three infinitely long charged thin sheets are placed as shown in figure. The magnitude of electric field at the point P is $\frac{x σ}{ε_{0}}$ . The value of $x$ is _____ (all quantities are measured in Sl units). [2024]

Q 3 :

A charge q is placed at the center of one of the surfaces of a cube. The flux linked with the cube is [2024]

Q 4 :

Five charges +q, +5q, −2q, +3q and −4q are situated as shown in the figure. The electric flux due to this configuration through the surface S is [2024]

Q 5 :

Two charges of 5Q and −2Q are situated at the points (3a,0) and (−5a,0) respectively. The electric flux through a sphere of radius 4a having center at origin is [2024]

Q 6 :

$C_{1}$ and $C_{2}$ are two hollow concentric cubes enclosing charges 2Q and 3Q respectively as shown in the figure. The ratio of electric flux passing through $C_{1}$ and $C_{2}$ is [2024]

Q 8 :

An electric field, $\vec{E} = \frac{2 \hat{i} + 6 \hat{j} + 8 \hat{k}}{\sqrt{6}}$ passes through the surface of $4 m^{2}$ area having unit vector $\hat{n} = (\frac{2 \hat{i} + \hat{j} + \hat{k}}{\sqrt{6}}) .$ The electric flux for that surface is ____ Vm. [2024]

Q 9 :

An electric field $\vec{E} = (2 x \hat{i}) N C^{- 1}$ exists in space. A cube of side 2 m is placed in the space as per figure given below. The electric flux through the cube is _____ ${Nm}^{2} / C .$ [2024]

Q 12 :

A point charge causes an electric flux of $- 2 \times 10^{4} {Nm}^{2} C^{- 1}$ to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is: (Given $ε_{0} = 8.85 \times 10^{- 12} C^{2} N^{- 1} m^{- 2}$ ) [2025]

Q 13 :

Consider two infinitely large plane parallel conducting plates as shown below. The plates are uniformly charged with a surface charge density $+ σ$ and $- 2 σ$ . The force experienced by a point charge $+ q$ placed at the midpoint between two plates will be: [2025]

Q 14 :

Two infinite identical charged sheets and a charged spherical body of charge density ' $ρ$ ' are arranged as shown in figure. Then the correct relation between the electrical fields at A, B, C and D points is: [2025]

Q 17 :

A square loop of sides a = 1 m is held normally in front of a point charge q = 1 C. The flux of the electric field through the shaded region is $\frac{5}{p} \times \frac{1}{ε_{0}} \frac{{Nm}^{2}}{C}$ , where the value of p is __________. [2025]

Q 18 :

The electric field in a region is given by $\vec{E} = (2 \hat{i} + 4 \hat{j} + 6 \hat{k}) \times 10^{3} N / C$ . The flux of the field through a rectangular surface parallel to x – z plane is 6.0 ${Nm}^{2} C^{- 1}$ . The area of the surface is __________ ${cm}^{2}$ . [2025]

Q 19 :

Let $σ$ be the uniform surface charge density of two infinite thin plane sheets shown in the figure. Then the electric fields in three different regions $E_{I}$ , $E_{I I}$ and $E_{I I I}$ is [2023]

Q 20 :

In a cuboid of dimension $2 L \times 2 L \times L$ , a charge $q$ is placed at the centre of the surface $' S'$ having area $4 L^{2}$ . The flux through the opposite surface to $' S'$ is given by [2023]

Q 21 :

As shown in the figure, a point charge $Q$ is placed at the centre of the conducting spherical shell of inner radius $a$ and outer radius $b$ . The electric field due to charge $Q$ in three different regions I, II and III is given by:

$(I: r < a, II: a < r < b, III: r > b)$ [2023]

Q 23 :

As shown in the figure, a cuboid lies in a region with electric field $\vec{E} = 2 x^{2} \hat{i} - 4 y \hat{j} + 6 \hat{k} N/C.$ The magnitude of charge within the cuboid is $n ε_{0} C$ . The value of $n$ is _______ (if dimensions of cuboid is $1 \times 2 \times 3 m^{3}$ ) [2023]

Q 24 :

Expression for an electric field is given by $\vec{E} = 4000 x^{2} \hat{i} V/m .$ The electric flux through the cube of side 20 cm when placed in the electric field (as shown in the figure) is ________ V cm. [2023]

Q 27 :

Two point charges $2 q$ and $q$ are placed at vertex A and centre of face CDEF of the cube as shown in the figure. The electric flux passing through the cube is: [2026]