A uniform electric field, E → = - 400 3 j ^ N C - 1 is applied in a region. A charged particle of mass m carrying positive charge q is projected in this region with an initial speed of 2 10 × 10 6 m s - 1 . This particle is aimed to hit a target T , which is 5 m away from its entry point into the field as shown schematically in the figure. Take q m = 10 10 C kg - 1 . Then

time taken by the particle to hit T could be 5 6 μ s as well as 5 2 μ s

the particle will hit T if projected at an angle 45 ° from the horizontal

time taken by the particle to hit T is 5 3 μ s

The electric field due to an extended charge distribution spread over all space is given by E → = q 4 π ε 0 r 2 1 + r λ e - r λ r ^ Here λ and q are positive constants and the electrostatic potential is taken to be zero at infinity. Select the correct statement(s).

There is a positive charge at the origin

The flux through a Gaussian sphere centred at the origin and of radius R decreases as we decrease R

EASY

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Electric field in a region is increasing in magnitude along $x$ -direction. The equipotential surfaces associated are

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Important Questions on Electrostatics

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

An infinitely long thin non-conducting wire is parallel to the z - axis and carries a uniform line charge density

λ

. It pierces a thin non-conducting spherical shell of radius

R

in such a way that the arc

P Q

subtends an angle

120^{o}

at the centre

O

of the spherical shell, as shown in the figure. The permittivity of free space is

ϵ_{0}

. Which of the following statements is (are) true?
Question Image

EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

What is the angle between maximum value of potential gradient and equipotential surface?

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

The angle between the electric lines of force and the equipotential surface is

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

Let

E_{1} (r), E_{2} (r)

and

E_{3} (r)

be the respective electric fields at a distance r from a point charge Q, an infinitely long wire with constant linear charge density

λ

, and an infinite plane with uniform surface charge density

σ

. If

E_{1} (r_{0}) = E_{2} (r_{0}) = E_{3} (r_{0})

at a given distance

r_{0}

, then

EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

The electric field lines on the left have twice the separation on those on the right as shown in figure. If the magnitude of the field at $A$ is $40 {Vm}^{- 1}$ , what is the force on $20 μ C$ charge kept at

Question Image

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

Two non-conducting spheres of radii $R_{1}$ and $R_{2}$ and carrying uniform volume charge densities $+ ρ$ and $- ρ$ , respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region,
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MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

Which statement(s) among the following are incorrect:
(i) A negative test charge experiences a force opposite to the direction of the field.
(ii) The tangent drawn to a line of force represents the direction of electric field.
(iii) The electric field lines never intersect.
(iv) The electric field lines form a closed loop.

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

A uniform electric field, $\vec{E} = - 400 \sqrt{3} \hat{j} N C^{- 1}$ is applied in a region. A charged particle of mass $m$ carrying positive charge $q$ is projected in this region with an initial speed of $2 \sqrt{10} \times 10^{6} m s^{- 1}$ . This particle is aimed to hit a target $T$ , which is $5 m$ away from its entry point into the field as shown schematically in the figure. Take $\frac{q}{m} = 10^{10} C {kg}^{- 1}$ . Then

Question Image

EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

Figure shows three arrangements of electric field lines. In each arrangement, a proton is released from rest at point A and then accelerated through point B by the electric field. Points A and B have equal separations in the three arrangements. If $p_{1}, p_{2}$ and $p_{3}$ are linear momentum of the proton at point B in the three arrangement respectively, then

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EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

The work done to move a charge on an equipotential surface is

EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

A long cylindrical shell carries positive surface charge

σ

in the upper half and negative surface charge

- σ

in the lower half. The electric field lines around the cylinder will look like figure given in:

(figures are schematic and not drawn to scale)

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

Within a spherical charge distribution of charge density

ρ (r),

N equipotential surfaces of potential

V_{0}, V_{0} + ∆ V, V_{0} + 2 ∆ V, \dots V_{0} + N ∆ V (∆ V > 0),

are drawn and have increasing radii

r_{0}, r_{1}, r_{2}, \dots r_{N},

respectively. If the difference in the radii of the surfaces is constant for all values of

V_{0} a n d ∆ V

then :

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

The figures below depict two situations in which two infinitely long static line charges of constant positive line charge density

λ

are kept parallel to each other. In their resulting electric field, point charges

q

and

- q

are kept in equilibrium between them. The point charges are confined to move in the

x

direction only. If they are given a small displacement about their equilibrium positions, then the correct statements(s) is (are)

Question Image

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

Two non-conducting solid spheres of radii $R$ and $2 R$ , having uniform volume charge densities $ρ_{1}$ and $ρ_{2}$ , respectively, touch each other. The net electric field at a distance $2 R$ from the centre of the smaller sphere, along the line joining the centres of the spheres, is zero. The ratio $\frac{ρ_{1}}{ρ_{2}}$ can be

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

Consider a uniform spherical charge distribution of radius

R_{1}

centred at the origin O. In this distribution, a spherical cavity of radius

R_{2}

, centred at

P

with distance

O P = a = R_{1} - R_{2}

(see figure) is made. If the electric field inside the cavity at position

\vec{r}

\vec{E} (\vec{r})

, then the correct statement(s) is (are)

Question Image

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

The electric field due to an extended charge distribution spread over all space is given by

\vec{E} = [\frac{q}{4 π ε_{0} r^{2}} (1 + \frac{r}{λ}) e^{- \frac{r}{λ}}] \hat{r}

Here

λ

and

q

are positive constants and the electrostatic potential is taken to be zero at infinity. Select the correct statement(s).

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

Two positive charges

Q

and

4 Q

are placed at points

A

and

B

respectively, where

B

is at a distance

d

units to the right of

A

. The total electric potential due to these charges is minimum at

P

on the line through

A

and

B

. What is (are) the distance (s) of

P

from

A

EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

Which is the INCORRECT statement regarding electric lines of force

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

A small point mass carrying some positive charge on it, is released from the edge of a table. There is a uniform electric field in this region in the horizontal direction. Which of the following options then correctly describe the trajectory of the mass ? (Curves are drawn schematically and are not to scale)

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

A point charge

+ Q

is placed just outside an imaginary hemispherical surface of radius R as shown in the figure. Which of the following statements is/are correct?

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Electric field in a region is increasing in magnitude along x-direction. The equipotential surfaces associated are

Important Questions on Electrostatics

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Electric field in a region is increasing in magnitude along $x$ -direction. The equipotential surfaces associated are