A system of three charges are placed as shown in the figure: If D > > d , the potential energy of the system is best given by:

1 4 π ϵ 0 - q 2 d - q Q d D 2

1 4 π ϵ 0 + q 2 d + q Q d D 2

1 4 π ϵ 0 - q 2 d - q Q d 2 D 2

1 4 π ϵ 0 - q 2 d + 2 q Q d D 2

Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Two metallic spheres are charged to the same potential. One of them is hollow and another is solid, and both have the same radii. Solid sphere will have lower charge than the hollow one. Reason R : Capacitance of metallic spheres depend on the radii of spheres. In the light of the above statements, choose the correct answer from the options given below.

Both A and R are true and R is the correct explanation of A

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

Let σ be the uniform surface charge density of two infinite thin plane sheets shown in figure. Then the electric fields in three different region E I , E I I and E I I I

E → I = - σ ∈ 0 n ^ , E → I I = 0 , E → I I I = σ ∈ 0 n ^

E → I = 2 σ ∈ 0 n ^ , E → I I = 0 , E → I I I = 2 σ ∈ 0 n ^

E → I = 0 , E → I I = σ ∈ 0 n ^ , E → I I I = 0

E → I = σ 2 ∈ 0 n ^ , E → I I = 0 , E → I I I = σ 2 ∈ 0 n ^

Considering a group of positive charges, which of the following statements is correct?

Net potential of the system cannot be zero at a point but net electric field can be zero at that point

Net potential of the system at a point can be zero but net electric field can't be zero at that point

Both the net potential and the net field can be zero at a point

Both the net potential and the net electric field cannot be zero at a point

HARD

JEE Main

IMPORTANT

Earn 100

A particle of mass $m$ and charge $q$ is released from rest in a uniform electric field. If there is no other force on the particle, the dependence of its speed $v$ on the distance $x$ travelled by it is correctly given by (graphs are schematic and not drawn to scale)

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Important Questions on Electrostatics

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 13 - Electrostatics>JEE Main - 9th January 2020 Shift 1>Q 84

Consider a sphere of radius

R

which carries a uniform charge density

ρ

. If a sphere of radius

\frac{R}{2}

is carved out of it, as shown, the ratio

\frac{|\vec{E_{A}}|}{|\vec{E_{B}}|}

of magnitude of electric field

\vec{E_{A}}

and

\vec{E_{B}}

, respectively, at points

A

and

B

due to the remaining portion is:

Question Image

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 13 - Electrostatics>JEE Main - 9th January 2020 Shift 1>Q 85

An electric dipole of moment

\vec{p} = (- \hat{i} - 3 \hat{j} + 2 \hat{k}) \times 10^{- 29} C m

at the origin

(0, 0, 0)

. The electric field due to this dipole at

\vec{r} = + \hat{i} + 3 \hat{j} + 5 \hat{k}

(note that

\vec{r} \cdot \vec{p} = 0

) is parallel to:

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 13 - Electrostatics>JEE Main - 9th January 2020 Shift 1>Q 86

A charged particle of mass

m

and charge

q

moving under the influence of uniform electric field

\vec{E} \hat{i}

and a uniform magnetic field

\vec{B} \hat{k}

follows a trajectory from point

P

Q

as shown in figure. The velocities at

P

and

Q

are respectively,

v \vec{i}

and

- 2 v \vec{j}

. Then which of the following statements (A, B, C, D) are the correct? (Trajectory shown is schematic and not to scale)

Question Image

(A)

E = \frac{3}{4} (\frac{m v^{2}}{q a})

(B)

Rate of work done by the electric field at P is

\frac{3}{4} (\frac{m v^{3}}{a})

(C)

Rate of work done by both the fields at Q is zero

(D)

The difference between the magnitude of angular momentum of the particle at P and Q is

2 m a v

HARD

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 13 - Electrostatics>JEE Main - 9th January 2020 Shift 2>Q 87

Two identical capacitors

A

and

B,

charged to the same potential

5 V

are connected in two different circuits as shown below at time

t = 0 .

If the charge on capacitors

A

and

B

at time

t = C R

Q_{A}

and

Q_{B}

respectively, then (Here

e

is the base of natural logarithm)

Question Image

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 13 - Electrostatics>JEE Main - 9th January 2020 Shift 2>Q 88

An electric field

\vec{E} = [4 x \hat{i} - (y^{2} + 1) \hat{j}] N C^{- 1}

passes through the box shown in figure. The flux of the electric field through surfaces

A B C D

and

B C G F

are marked as

ϕ_{I}

and

ϕ_{I I}

respectively. The value of

|ϕ_{I} - ϕ_{I I}|

is (in

N m^{2} C^{- 1}

) ____________.
Question Image

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 13 - Electrostatics>JEE Main - 9th April 2019 Shift 1>Q 89

A capacitor with capacitance

5 μ F

is charged to

5 μ C

. If the plates are pulled apart to reduce the capacitance to

2 μ F

, how much work is done?

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 13 - Electrostatics>JEE Main - 9th April 2019 Shift 1>Q 90

A system of three charges are placed as shown in the figure:
Question Image

D > > d,

the potential energy of the system is best given by:

MEDIUM

JEE Main

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR PHYSICS>Chapter 13 - Electrostatics>JEE Main - 9th April 2019 Shift 1>Q 91

Determine the charge on the capacitor in the following circuit:
Question Image

A particle of mass m and charge q is released from rest in a uniform electric field. If there is no other force on the particle, the dependence of its speed v on the distance x travelled by it is correctly given by (graphs are schematic and not drawn to scale)

Important Questions on Electrostatics

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A particle of mass $m$ and charge $q$ is released from rest in a uniform electric field. If there is no other force on the particle, the dependence of its speed $v$ on the distance $x$ travelled by it is correctly given by (graphs are schematic and not drawn to scale)