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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(C) 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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(B) 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)

[IMAGE 127]

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

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)

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

[IMAGE 128]

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

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

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

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)

[IMAGE 129]

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

[IMAGE 130]

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

[IMAGE 131]

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

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

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

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

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

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 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]