Electric Field and Charge Particle in Electric Field

Q 1 :

An infinitely long positively charged straight thread has a linear charge density $λ$ $C m^{- 1}$ . An electron revolves along a circular path having axis along the length of the wire. The graph that correctly represents the variation of the kinetic energy of electron as a function of radius of circular path from the wire is [2024]

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(2)

Electric field E at a distance r due to infinite long wire is $E = \frac{2 k λ}{r}$

Force of electron, $F = e E \Rightarrow F = e (\frac{2 k λ}{r}) = \frac{2 k λ e}{r}$

This force will provide the required centripetal force.

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

$K E = \frac{1}{2} m v^{2} = \frac{1}{2} m (\frac{2 k λ e}{m}) = k λ e = constant$

Q 2 :

$σ$ is the uniform surface charge density of a thin spherical shell of radius R. The electric field at any point on the surface of the spherical shell is: [2024]

$\frac{σ}{ε_{0} R}$
$\frac{σ}{ε_{0}}$
$\frac{σ}{2 ε_{0}}$
$\frac{σ}{4 ε_{0}}$

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(2)

By Gauss law $\int \vec{E} \cdot d \vec{A} = \frac{q_{in}}{ε_{0}}$

$E d A = \frac{σ \times d A}{ε_{0}} \Rightarrow E = \frac{σ}{ε_{0}}$

Q 3 :

A particle of charge ‘−q’ and mass ‘m’ moves in a circle of radius ‘r’ around an infinitely long line charge of linear density ‘ $+ λ$ ’. Then time period will be given as

(Consider k as Coulomb’s constant) [2024]

$T^{2} = \frac{4 π^{2} m}{2 k λ q} r^{3}$
$T = 2 π r \sqrt{\frac{m}{2 k λ q}}$
$T = \frac{1}{2 π r} \sqrt{\frac{m}{2 k λ q}}$
$T = \frac{1}{2 π} \sqrt{\frac{2 k λ q}{m}}$

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(2)

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

$q (\frac{2 K λ}{r}) = \frac{m v^{2}}{r} \Rightarrow v = \sqrt{\frac{2 K q λ}{m}}$

$T = \frac{2 π r}{v} = \frac{2 π r}{\sqrt{\frac{2 K q λ}{m}}} = 2 π r \sqrt{\frac{m}{2 K q λ}}$

Q 4 :

Two charges q and 3q are separated by a distance ‘r’ in air. At a distance x from charge q, the resultant electric field is zero. The value of x is [2024]

$\frac{r}{(1 + \sqrt{3})}$
$\frac{(1 + \sqrt{3})}{r}$
$r (1 + \sqrt{3})$
$\frac{r}{3 (1 + \sqrt{3})}$

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(1)

${({\vec{E}}_{net})}_{P} = 0 \Rightarrow \frac{k q}{x^{2}} = \frac{k \cdot 3 q}{{(r - x)}^{2}}$

${(r - x)}^{2} = 3 x^{2}$

$r - x = \sqrt{3} x \Rightarrow x = \frac{r}{\sqrt{3} + 1}$

Q 5 :

If the net electric field at point P along Y axis is zero, then the ratio of $| \frac{q_{2}}{q_{3}} |$ is $\frac{8}{5 \sqrt{x}}$ , where $x$ = ______ . [2024]

(5)

$\frac{K q_{2}}{{(\sqrt{20})}^{2}} \cos β = \frac{K q_{3}}{{(5)}^{2}} \cos θ$

$\frac{K q_{2}}{20} \frac{4}{\sqrt{20}} = \frac{K q_{3}}{25} \frac{4}{\sqrt{25}}$

$\frac{q_{2}}{q_{3}} = \frac{20}{25} \frac{\sqrt{20}}{\sqrt{25}} = \frac{8}{5 \sqrt{x}}$

$\Rightarrow \sqrt{x} = \frac{8 \times 25 \sqrt{25}}{5 \times 20 \sqrt{20}} \Rightarrow x = 5$

Q 6 :

An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet S having surface charge density $+ σ$ . The electron at t = 0 is at a distance of 1 m from S and has a speed of 1 m/s. The maximum value of $σ$ if the electron strikes S at t = 1s is $α [\frac{m ε_{0}}{e}] \frac{C}{m^{2}},$ the value of $α$ is _________ . [2024]

(8)

Initially the electron must move away from sheet

Electric field due to infinite plane sheet of charge,

$E = \frac{σ}{2 ε_{0}}$

Force experienced by the electron towards the sheet, $F = e E$

Hence, acceleration of the electron, $a = \frac{F}{m}$

$a = \frac{e E}{m} = \frac{e σ}{2 ε_{0} m}$

Using $s = u t + \frac{1}{2} a t^{2}$

$- 1 = 1 \times 1 + \frac{1}{2} (- \frac{e σ}{2 ε_{0} m}) 1^{2}$

$\frac{e σ}{4 ε_{0} m} = 2 \Rightarrow σ = 8 \frac{ε_{0} m}{e}$

Q 7 :

Suppose a uniformly charged wall provides a uniform electric field of $2 \times 10^{4}$ N/C normally. A charged particle of mass 2g being suspended through a silk thread of length 20 cm and remains stayed at a distance of 10 cm from the wall. Then the charge on the particle will be $\frac{1}{\sqrt{x}} μ C$ where $x =$ __________. [use g = 10 $m / s^{2}$ ] [2024]

(3)

$\sin θ = \frac{10}{20} = \frac{1}{2} \Rightarrow θ = 30 °$

Along x-axis

$\sum {(f_{net})}_{y} = 0 (for equilibrium)$

$T \sin θ = q E$ ...(i)

Along y-axis

$\sum {(f_{net})}_{x} = 0 (for equilibrium)$

$T \cos θ = m g$ ...(ii)

From (i) divide by (ii), $\tan θ = \frac{q E}{m g}$

$q = \frac{m g \tan θ}{E}$

$= \frac{2 \times 10^{- 3} \times 10}{2 \times 10^{4}} \times \frac{1}{\sqrt{3}} = \frac{10^{- 6}}{\sqrt{3}} C$

$\Rightarrow q = \frac{1}{\sqrt{3}} μ C \Rightarrow x = 3$

Q 8 :

An electron is made to enters symmetrically between two parallel and equally but oppositely charged metal plates, each of 10 cm length. The electron emerges out of the field region with a horizontal component of velocity $10^{6}$ m/s. If the magnitude of the electric field between the plates is 9.1 V/cm, then the vertical component of velocity of electron is (mass of electron = $9.1 \times 10^{- 31} kg$ and charge of electron = $1.6 \times 10^{- 19}$ ) [2025]

$1 \times 10^{6} m / s$
0
$16 \times 10^{6} m$
$16 \times 10^{4} m / s$

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(3)

Horizontal component of velocity will remain same.

$\Rightarrow t = \frac{l}{V_{x}} = \frac{10 \times 10^{- 2}}{10^{6}} = 10^{- 7}$

$\Rightarrow V_{y} = u_{y} + a_{y} t \Rightarrow V_{y} = 0 + \frac{e E}{m} \times 10^{- 7}$

$\Rightarrow V_{y} = \frac{1.6 \times 10^{- 19}}{9.1 \times 10^{- 31}} \times 9.1 \times 10^{+ 2} \times 10^{- 7}$

$\Rightarrow V_{y} = 16 \times 10^{6} m / s$

Q 9 :

A particle of mass 'm' and charge 'q' is fastened to one end 'A' of a massless string having equilibrium length $l$ , whose other end is fixed at point 'O'. The whole system is placed on a frictionless horizontal plane and is initially at rest. If uniform electric field is switched on along the direction as shown in figure, then the speed of the particle when it crosses the x-axis is [2025]

$\sqrt{\frac{2 q E l}{m}}$
$\sqrt{\frac{q E l}{4 m}}$
$\sqrt{\frac{q E l}{m}}$
$\sqrt{\frac{q E l}{2 m}}$

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(3)

From work energy theorem,

Work done by electric force = change in kinetic energy or

$q E (l - l \cos 60 °) = \frac{1}{2} m v^{2}$

$\Rightarrow \frac{q E l}{2} = \frac{1}{2} m v^{2} or v = \sqrt{\frac{q E l}{m}}$

Q 10 :

A point charge +q is placed at the origin. A second point charge +9q is placed at (d, 0, 0) in Cartesian coordinate system. The point in between them where the electric field vanishes is: [2025]

(4d/3, 0 , 0)
(d/4, 0 , 0)
(3d/4, 0 , 0)
(d/3, 0 , 0)

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(2)

Let $E_{P} = 0$

$∴ \frac{k q}{x^{2}} = \frac{k 9 q}{{(d - x)}^{2}} \Rightarrow \frac{d - x}{x} = 3 \Rightarrow x = \frac{d}{4}$

$∴$ co-ordinate of P is $(\frac{d}{4}, 0, 0)$

Q 11 :

A small bob of mass 100 mg and charge +10 $μ$ C is connected to an insulating string of length 1 m. It is brought near to an infinitely long non-conducting sheet of charge density ' $σ$ ' as shown in figure. If string subtends an angle of 45° with the sheet at equilibrium the charge density of sheet will be:

(Given, $ε_{0} = 8.85 \times 10^{- 12} \frac{F}{m}$ and acceleration due to gravity, $g = 10 m / s^{2}$ ) [2025]

0.885 $nC / m^{2}$
17.7 $nC / m^{2}$
885 $nC / m^{2}$
1.77 $nC / m^{2}$

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(4)

T sin 45° = Eq

T cos 45° = mg

$Eq = mg$

$E = \frac{m g}{q} = \frac{σ}{2 ε_{0}}$

$σ = \frac{2 ε_{0} m g}{q} = 1.77 nC / m^{2}$

Q 12 :

Consider a circular loop that is uniformly charged and has a radius $a \sqrt{2}$ . Find the position along the positive z-axis of the cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in xy-plane at the origin: [2025]

$\frac{a}{\sqrt{2}}$
$\frac{a}{2}$
a
0

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(3)

$E = K \frac{Q r}{{(x^{2} + R^{2})}^{3 / 2}}$

For $E_{\max}, \frac{d E}{d x} = 0$

$∴ x = \frac{R}{\sqrt{2}} = \frac{\sqrt{2} a}{\sqrt{2}} = a$

Q 13 :

A metallic ring is uniformly charged as shown in figure. AC and BD are two mutually perpendicular diameters. Electric field due to arc AB to 'O' is 'E' in magnitude. What would be the magnitude of electric field at 'O' due to arc ABC? [2025]

2 E
$\sqrt{2} E$
E/2
Zero

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(2)

Q 14 :

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

Assertion (A) : The outer body of an air craft is made of metal which protects persons sitting inside from lightning strikes.

Reason (R) : The electric field inside the cavity enclosed by a conductor is zero.

In the light of the above statements, choose the most appropriate answer from the options given below: [2025]

Both (A) and (R) are correct and (R) is the correct explanation of (A)
(A) is correct but (R) is not correct
Both (A) and (R) are correct but (R) is not the correct explanation of (A)
(A) is not correct but (R) is correct

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(1)

The outer body of aircraft is made with metal to provide electrostatic shielding such that electric field inside craft remain zero for any charge on outer surface.

Q 15 :

Electric charge is transferred to an irregular metallic disk as shown in figure. If $σ_{1}, σ_{2}, σ_{3}$ and $σ_{4}$ are charge densities at given points then, choose the correct answer from the options given below: [2025]

(A) $σ_{1} > σ_{3}; σ_{2} = σ_{4}$

(B) $σ_{1} > σ_{2}; σ_{3} > σ_{4}$

(C) $σ_{1} > σ_{3} > σ_{2} = σ_{4}$

(D) $σ_{1} > σ_{2}; σ_{3} = σ_{4}$

(E) $σ_{1} = σ_{2} = σ_{3} = σ_{4}$

A, B and C Only
A and C Only
D and E Only
B and C Only

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(1)

$σ \propto \frac{1}{R} R \to radius of curvature$

$R_{2} = R_{4} > R_{3} > R_{1}$

$\Rightarrow σ_{1} > σ_{3} > σ_{4} = σ_{2}$

Q 16 :

Electric field in a certain region is given by $\vec{E} = (\frac{A}{x^{2}} \hat{i} + \frac{B}{y^{3}} \hat{j}) .$ The SI unit of $A$ and $B$ are [2023]

${Nm}^{3} C^{- 1}; {Nm}^{2} C^{- 1}$
${Nm}^{2} C^{- 1}; {Nm}^{3} C^{- 1}$
${Nm}^{3} C; {Nm}^{2} C$
${Nm}^{2} C; {Nm}^{3} C$

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(2)

$\vec{E} = \frac{A}{x^{2}} \hat{i} + \frac{B}{y^{3}} \hat{j}$

$[\frac{A}{x^{2}}] = {NC}^{- 1} \Rightarrow [A] = {Nm}^{2} C^{- 1}$

$[\frac{B}{y^{3}}] = {NC}^{- 1} \Rightarrow [B] = {Nm}^{3} C^{- 1}$

Q 17 :

Graphical variation of electric field due to a uniformly charged insulating solid sphere of radius $R$ , with distance $r$ from the centre $O$ is represented by [2023]

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(4)

$Electric field of solid sphere (uniformly charged)$

$E (r)$ ${\begin{matrix} \frac{Q}{4 π ε_{0} r^{2}}, & r \geq R \\ \frac{Q r}{4 π ε_{0} R^{3}}, & r \leq R \end{matrix}$

$Graphically, E (r) \propto r for r \leq R$

Q 18 :

A stream of positively charged particles having $\frac{q}{m} = 2 \times 10^{11} \frac{C}{kg}$ and velocity ${\vec{v}}_{0} = 3 \times 10^{7} \hat{i} m/s$ deflected by an electric field $1.8 \hat{j} kV/m .$ The electric field exists in a region of 10 cm along the $x$ -direction. Due to the electric field, the deflection of the charged particles in the $y$ -direction is ________ mm. [2023]

(2)

$a = \frac{F}{m} = \frac{q E}{m} = (2 \times 10^{11}) (1.8 \times 10^{3}) = 3.6 \times 10^{14} {m/s}^{2}$

$Time to cross plates t = \frac{d}{v}$

$t = \frac{0.10}{3 \times 10^{7}}$

$y = \frac{1}{2} a t^{2} = \frac{1}{2} (3.6 \times 10^{14}) {(\frac{0.01}{9 \times 10^{14}})}^{2}$

$= 0.2 \times 0.01 = 0.002 m = 2 mm$

Q 19 :

A uniform electric field of 10 N/C is created between two parallel charged plates (as shown in fig). An electron enters the field symmetrically between the plates with a kinetic energy 0.5 eV. The length of each plate is 10 cm. The angle $(θ)$ of deviation of the path of electron as it comes out of the field is ________ (in degree). [2023]

(45)

$l = u t$

$t = \frac{l}{u}$

$\tan θ = \frac{v_{y}}{u} = \frac{a t}{u} = \frac{E q}{m} \frac{l}{u^{2}} = \frac{E q l}{2 (\frac{1}{2} m u^{2})} = \frac{E q l}{2 K.E.}$

$\tan θ = \frac{10 \times 1.6 \times 10^{- 19} \times 0.1}{2 \times 0.5 \times 1.6 \times 10^{- 19}} = 1 \Rightarrow θ = 45 °$

Q 20 :

Two equal positive point charges are separated by a distance $2 a$ . The distance of a point from the centre of the line joining the two charges on the equatorial line (perpendicular bisector), at which the force experienced by a test charge $q_{0}$ becomes maximum, is $\frac{a}{\sqrt{x}} .$ The value of $x$ is __________ . [2023]

(2)

$F = \frac{2 K q q_{0} x}{{(x^{2} + a^{2})}^{3 / 2}}$

$For F to be maximum, \frac{d F}{d x} = 0$

$\Rightarrow x = \frac{a}{\sqrt{2}}$

Q 21 :

As shown in the figure, a configuration of two equal point charges ( $q_{0} = + 2 μ C$ ) is placed on an inclined plane. The mass of each point charge is 20 g. Assume that there is no friction between the charge and the plane. For the system of two point charges to be in equilibrium (at rest), the height $h = x \times 10^{- 3} m .$ The value of $x$ is ______.

(Take $\frac{1}{4 π ε_{0}} = 9 \times 10^{9} {N m}^{2} C^{- 2},$ $g = 10 {ms}^{- 1}$ ) [2023]

(300)

$For equilibrium along the plane$

$m g \sin θ = \frac{1}{4 π ε_{0}} \times \frac{q_{0}^{2}}{{(h \cos e c 30 °)}^{2}}$

$∴$ $h^{2} = \frac{1}{4 π ε_{0}} \times \frac{q_{0}^{2}}{m g cosec 30 °} = 9 \times 10^{9} \times \frac{{(2 \times 10^{- 6})}^{2}}{0.02 \times 10 \times 2}$

$∴$ $h = 3 \times 10^{4} \times \frac{2 \times 10^{- 6}}{2} = 0.3 m = 300 mm$

Q 22 :

Six point charges are kept $60 °$ apart from each other on the circumference of a circle of radius R as shown in figure. The net electric field at the center of the circle is ______.

( $ε_{0}$ is permittivity of free space) [2026]

$- (\frac{5 Q}{8 π ε_{0} R^{2}}) (\hat{i} - 3 \hat{j})$
$\frac{Q}{4 π ε_{0} R^{2}} (\sqrt{3} \hat{i} - \hat{j})$
$- \frac{5 Q}{8 π ε_{0} R^{2}} (\hat{i} + \sqrt{3} \hat{j})$
$- \frac{Q}{4 π ε_{0} R^{2}} (\sqrt{3} \hat{i} - \hat{j})$

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(4)

$Let \frac{k Q}{r^{2}} = E_{0}$

${\vec{E}}_{net} = 2 E_{0} \cos 30 ° (- \hat{i}) + 2 E_{0} \sin 30 ° (\hat{j})$

$= \frac{2 k Q}{r^{2}} [\frac{\sqrt{3}}{2} (- \hat{i}) + \frac{1}{2} \hat{j}]$

$= \frac{- Q}{4 π ε_{0} r^{2}} (\sqrt{3} \hat{i} - \hat{j})$

Q 23 :

A simple pendulum has a bob with mass $m$ and charge $q$ . The pendulum string has negligible mass. When a uniform and horizontal electric field $\vec{E}$ is applied, the tension in the string changes. The final tension in the string, when the pendulum attains an equilibrium position, is _______.

(g = acceleration due to gravity) [2026]

$m g - q E$
$m g + q E$
$\sqrt{m^{2} g^{2} - q^{2} E^{2}}$
$\sqrt{m^{2} g^{2} + q^{2} E^{2}}$

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(4)

$T = \sqrt{{(q E)}^{2} + {(m g)}^{2}}$

Q 24 :

Identify the correct statements:

A. Electrostatic field lines form closed loops.
B. The electric field lines point radially outward when charge is greater than zero.
C. The Gauss–Law is valid only for inverse-square force.
D. The workdone in moving a charged particle in a static electric field around a closed path is zero.
E. The motion of a particle under Coulomb’s force must take place in a plane.

Choose the correct answer from the options given below: [2026]

A, B, C, D Only
A, C, E Only
A, B, D, E Only
B, C, D, E Only

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(4)

Static electric field lines do NOT from closed loops (they start on positive and end on negative charges), making statement A false.

Q 25 :

If $ε, E$ and t represent the free space permittivity, electric field and time respectively, then the unit of $\frac{ε E}{t}$ will be : [2026]

$A m$
$A / m ²$
$A / m$
$A m ²$

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(2)

$\frac{ε E}{t} = \frac{ε}{t} \frac{1}{4 π ε} \frac{q}{r^{2}}$

$\Rightarrow \frac{A T}{T L^{2}} = (A L^{- 2})$

$\Rightarrow {A/m}^{2}$

Topic Question Set

Q 2 :

$σ$ is the uniform surface charge density of a thin spherical shell of radius R. The electric field at any point on the surface of the spherical shell is: [2024]

Q 3 :

A particle of charge ‘−q’ and mass ‘m’ moves in a circle of radius ‘r’ around an infinitely long line charge of linear density ‘ $+ λ$ ’. Then time period will be given as

(Consider k as Coulomb’s constant) [2024]

Q 4 :

Two charges q and 3q are separated by a distance ‘r’ in air. At a distance x from charge q, the resultant electric field is zero. The value of x is [2024]

Q 5 :

If the net electric field at point P along Y axis is zero, then the ratio of $| \frac{q_{2}}{q_{3}} |$ is $\frac{8}{5 \sqrt{x}}$ , where $x$ = ______ . [2024]

Q 10 :

A point charge +q is placed at the origin. A second point charge +9q is placed at (d, 0, 0) in Cartesian coordinate system. The point in between them where the electric field vanishes is: [2025]

Q 12 :

Consider a circular loop that is uniformly charged and has a radius $a \sqrt{2}$ . Find the position along the positive z-axis of the cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in xy-plane at the origin: [2025]

Q 13 :

A metallic ring is uniformly charged as shown in figure. AC and BD are two mutually perpendicular diameters. Electric field due to arc AB to 'O' is 'E' in magnitude. What would be the magnitude of electric field at 'O' due to arc ABC? [2025]

Q 16 :

Electric field in a certain region is given by $\vec{E} = (\frac{A}{x^{2}} \hat{i} + \frac{B}{y^{3}} \hat{j}) .$ The SI unit of $A$ and $B$ are [2023]

Q 17 :

Graphical variation of electric field due to a uniformly charged insulating solid sphere of radius $R$ , with distance $r$ from the centre $O$ is represented by [2023]

Q 22 :

Six point charges are kept $60 °$ apart from each other on the circumference of a circle of radius R as shown in figure. The net electric field at the center of the circle is ______.

( $ε_{0}$ is permittivity of free space) [2026]

Q 25 :

If $ε, E$ and t represent the free space permittivity, electric field and time respectively, then the unit of $\frac{ε E}{t}$ will be : [2026]

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Topic Question Set

Q 2 : σ is the uniform surface charge density of a thin spherical shell of radius R. The electric field at any point on the surface of the spherical shell is: [2024]

Q 3 : A particle of charge ‘−q’ and mass ‘m’ moves in a circle of radius ‘r’ around an infinitely long line charge of linear density ‘+λ’. Then time period will be given as (Consider k as Coulomb’s constant) [2024]

Q 4 : Two charges q and 3q are separated by a distance ‘r’ in air. At a distance x from charge q, the resultant electric field is zero. The value of x is [2024]

Q 5 : If the net electric field at point P along Y axis is zero, then the ratio of |q2q3| is 85x, where x = ______ . [2024]

Q 10 : A point charge +q is placed at the origin. A second point charge +9q is placed at (d, 0, 0) in Cartesian coordinate system. The point in between them where the electric field vanishes is: [2025]

Q 12 : Consider a circular loop that is uniformly charged and has a radius a2. Find the position along the positive z-axis of the cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in xy-plane at the origin: [2025]

Q 13 : A metallic ring is uniformly charged as shown in figure. AC and BD are two mutually perpendicular diameters. Electric field due to arc AB to 'O' is 'E' in magnitude. What would be the magnitude of electric field at 'O' due to arc ABC? [2025]

Q 16 : Electric field in a certain region is given by E→=(Ax2 i^+By3 j^). The SI unit of A and B are [2023]

Q 17 : Graphical variation of electric field due to a uniformly charged insulating solid sphere of radius R, with distance r from the centre O is represented by [2023]

Q 22 : Six point charges are kept 60° apart from each other on the circumference of a circle of radius R as shown in figure. The net electric field at the center of the circle is ______. (ε0 is permittivity of free space) [2026]

Q 25 : If ε,E and t represent the free space permittivity, electric field and time respectively, then the unit of εEt will be : [2026]

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Q 2 :

$σ$ is the uniform surface charge density of a thin spherical shell of radius R. The electric field at any point on the surface of the spherical shell is: [2024]

Q 3 :

A particle of charge ‘−q’ and mass ‘m’ moves in a circle of radius ‘r’ around an infinitely long line charge of linear density ‘ $+ λ$ ’. Then time period will be given as

(Consider k as Coulomb’s constant) [2024]

Q 4 :

Two charges q and 3q are separated by a distance ‘r’ in air. At a distance x from charge q, the resultant electric field is zero. The value of x is [2024]

Q 5 :

If the net electric field at point P along Y axis is zero, then the ratio of $| \frac{q_{2}}{q_{3}} |$ is $\frac{8}{5 \sqrt{x}}$ , where $x$ = ______ . [2024]

Q 10 :

A point charge +q is placed at the origin. A second point charge +9q is placed at (d, 0, 0) in Cartesian coordinate system. The point in between them where the electric field vanishes is: [2025]

Q 12 :

Consider a circular loop that is uniformly charged and has a radius $a \sqrt{2}$ . Find the position along the positive z-axis of the cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in xy-plane at the origin: [2025]

Q 13 :

A metallic ring is uniformly charged as shown in figure. AC and BD are two mutually perpendicular diameters. Electric field due to arc AB to 'O' is 'E' in magnitude. What would be the magnitude of electric field at 'O' due to arc ABC? [2025]

Q 16 :

Electric field in a certain region is given by $\vec{E} = (\frac{A}{x^{2}} \hat{i} + \frac{B}{y^{3}} \hat{j}) .$ The SI unit of $A$ and $B$ are [2023]

Q 17 :

Graphical variation of electric field due to a uniformly charged insulating solid sphere of radius $R$ , with distance $r$ from the centre $O$ is represented by [2023]

Q 22 :

Six point charges are kept $60 °$ apart from each other on the circumference of a circle of radius R as shown in figure. The net electric field at the center of the circle is ______.

( $ε_{0}$ is permittivity of free space) [2026]

Q 25 :

If $ε, E$ and t represent the free space permittivity, electric field and time respectively, then the unit of $\frac{ε E}{t}$ will be : [2026]