Electric Charge and Field | Physics JEE previous year questions with Solutions

Q 1 :
The vehicles carrying inflammable fluids usually have metallic chains touching the ground [2024]

to alert other vehicles
it is a custom
to conduct excess charge due to air friction to ground and prevent sparking
to protect tyres from catching dirt from ground

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(3)

Due to friction, fluids get charged, this can result in combustion.

So, metallic chains is used to discharge excess charge.

Q 2 :
Force between two point charges $q_{1}$ and $q_{2}$ placed in vacuum at $' r'$ cm apart is F. Force between them when placed in a medium having dielectric $K = 5$ at $r / 5$ cm apart will be: [2024]

F/25
5F
F/5
25F

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(2)

In air $F = \frac{1}{4 π \in_{0}} \frac{q_{1} q_{2}}{r^{2}}$

In medium

$F' = \frac{1}{4 π (K \in_{0})} \frac{q_{1} q_{2}}{{(r')}^{2}} = \frac{25}{4 π (5 \in_{0})} \frac{q_{1} q_{2}}{{(r)}^{2}} = 5 F$

Q 3 :
Two identical conducting spheres P and S with charge Q on each, repel each other with a force 16 N. A third identical uncharged conducting sphere R is successively brought in contact with the two spheres. The new force of repulsion between P and S is: [2024]

4 N
1 N
6 N
12 N

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(3)

$F_{1} = \frac{K Q^{2}}{r^{2}} = 16$ ...(i)

$F_{2} = \frac{K \frac{Q}{2} \cdot \frac{3 Q}{4}}{r^{2}} = \frac{3}{8} \cdot \frac{K Q^{2}}{r^{2}} = \frac{3}{8} \times 16 = 6 N$

Q 4 :
A thin metallic wire having cross-sectional area of $10^{- 4}$ $m^{2}$ is used to make a ring of radius 30 cm. A positive charge of $2 π$ C is uniformly distributed over the ring, while another positive charge of 30 pC is kept at the centre of the ring. The tension in the ring is ____ N; provided that the ring does not get deformed (neglect the influence of gravity).

(Given, $\frac{1}{4 π ϵ_{0}} = 9 \times 10^{9}$ in SI units) [2024]

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(3)

$2 T \sin \frac{d θ}{2} = \frac{k q_{0}}{R^{2}} \cdot λ R d θ$ $[λ = \frac{Q}{2 π R}]$

$\Rightarrow T = \frac{k q_{0} Q}{(R^{2}) \times 2 π}$

$= \frac{(9 \times 10^{9}) (2 π \times 30 \times 10^{- 12})}{{(0.30)}^{2} \times 2 π}$

$= \frac{9 \times 10^{- 3} \times 30}{9 \times 10^{- 2}} = 3 N$

Q 5 :
Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle $θ$ with each other. When suspended in water, the angle remains the same. If the density of the material of the sphere is 1.5 g/cc, the dielectric constant of water will be ______.

(Take density of water = 1 g/cc) [2024]

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(3)

$\tan θ = \frac{K Q^{2}}{{(2 l \sin θ)}^{2} \times ρ v g}$ ...(i)

$\tan θ = \frac{K Q^{2}}{ε {(2 l \sin θ)}^{2} \times (ρ v - ρ_{w} v) g}$ ...(ii)

Compare (i) and (ii)

$ε (ρ v - ρ_{w} v) g = ρ v g$

$ε = \frac{1.5}{1.5 - 1} = \frac{1.5}{0.5} = 3$

Q 6 :
Two identical charged spheres are suspended by string of equal lengths. The string make an angle of 37° with each other. When suspended in a liquid of density 0.7 $g / {cm}^{3}$ , the angle remains same. If density of material of the sphere is 1.4 $g / {cm}^{3}$ , the dielectric constant of the liquid is $(\tan 37^{o} = \frac{3}{4})$ ______________ . [2024]

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(2)

$\tan θ = \frac{F_{e}}{m g}$ ...(1)

$\tan θ = \frac{F_{e} / K}{(m g - B)}$ ...(2)

$\frac{F_{e}}{K (m g - B)} = \frac{F_{e}}{m g}$

$K (m g - B) = m g$

$K (σ_{m} V g - ρ_{ℓ} V g) = σ_{m} V g$

$V k g [1.4 - 0.7] = 1.4 k g$

$K = \frac{1.4}{0.7} = 2$

Q 7 :
A small uncharged conducting sphere is placed in contact with an identical sphere but having $4 \times 10^{- 8} C$ charge and then removed a distance such that the force of repulsion between them is $9 \times 10^{- 3} N$ .

The distance between them is (Take $\frac{1}{4 π ε_{0}}$ as $9 \times 10^{9}$ in SI units) [2025]

2 cm
3 cm
4 cm
1 cm

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(1)

Figure

$F = \frac{k (\frac{Q}{2}) (\frac{Q}{2})}{r^{2}}$

$9 \times 10^{- 3} = \frac{9 \times 10^{9} \times (4 \times 10^{- 8}) \times 4 \times 10^{- 8}}{4 \times 9 \times 10^{- 3}}$

$r^{2} = \frac{9 \times 10^{9} \times 16 \times 10^{- 16}}{4 \times 9 \times 10^{- 3}} = 4 \times 10^{- 4}$

$r^{2} = 2 \times 10^{- 2} m = 2 cm$

Q 8 :
A positive ion A and a negative ion B has charges $6.67 \times 10^{- 19} C$ and $9.647 \times 10^{- 10} C$ , and masses $19.2 \times 10^{- 27} kg$ and $9 \times 10^{- 27} kg$ respectively. At an instant, the ions are separated by a certain distance r. At that instant the ratio of the magnitudes of electrostatic force to gravitational force is $P \times 10^{- 13}$ , where the value of P is __________.

Take $\frac{1}{4 π ε_{0}} = 9 \times 10^{9} {Nm}^{2} C^{- 1}$ and universal gravitational constant as $6.67 \times 10^{- 11} {Nm}^{2} {kg}^{- 2}$ ) [2025]

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(Bonus)

$F_{2} = \frac{k q_{1} q_{2}}{r^{2}} and F_{g} = \frac{G m_{1} m_{2}}{r^{2}}$

$\frac{F_{2}}{F_{g}} = \frac{k q_{1} q_{2}}{G m_{1} m_{2}}$

$= \frac{9 \times 10^{9} \times 6.67 \times 10^{- 19} \times 9.6 \times 10^{- 10}}{6.67 \times 10^{- 11} \times 19.2 \times 10^{- 27} \times 9 \times 10^{- 27}}$

$= \frac{10^{- 20}}{2 \times 10^{- 65}} = \frac{1}{2} \times 10^{45}$

Topic Question Set

Q 1 :
The vehicles carrying inflammable fluids usually have metallic chains touching the ground [2024]

Q 2 :
Force between two point charges $q_{1}$ and $q_{2}$ placed in vacuum at $' r'$ cm apart is F. Force between them when placed in a medium having dielectric $K = 5$ at $r / 5$ cm apart will be: [2024]

Q 3 :
Two identical conducting spheres P and S with charge Q on each, repel each other with a force 16 N. A third identical uncharged conducting sphere R is successively brought in contact with the two spheres. The new force of repulsion between P and S is: [2024]

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Topic Question Set

Q 1 : The vehicles carrying inflammable fluids usually have metallic chains touching the ground [2024]

Q 2 : Force between two point charges q1 and q2 placed in vacuum at 'r' cm apart is F. Force between them when placed in a medium having dielectric K=5 at r/5 cm apart will be: [2024]

Q 3 : Two identical conducting spheres P and S with charge Q on each, repel each other with a force 16 N. A third identical uncharged conducting sphere R is successively brought in contact with the two spheres. The new force of repulsion between P and S is: [2024]

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Q 7 : A small uncharged conducting sphere is placed in contact with an identical sphere but having 4×10–8 C charge and then removed a distance such that the force of repulsion between them is 9×10–3 N. The distance between them is (Take 14πε0 as 9×109 in SI units) [2025]

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Q 1 :
The vehicles carrying inflammable fluids usually have metallic chains touching the ground [2024]

Q 2 :
Force between two point charges $q_{1}$ and $q_{2}$ placed in vacuum at $' r'$ cm apart is F. Force between them when placed in a medium having dielectric $K = 5$ at $r / 5$ cm apart will be: [2024]

Q 3 :
Two identical conducting spheres P and S with charge Q on each, repel each other with a force 16 N. A third identical uncharged conducting sphere R is successively brought in contact with the two spheres. The new force of repulsion between P and S is: [2024]