Electric Field

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JEE Main 2021

Find the electric field at point P (as shown in figure) on the perpendicular bisector of a uniformly charged thin wire of length $L$ carrying a charge $Q$ . The distance of the point P from the centre of the rod is $a = \frac{3}{2} L$ .

\frac{3 Q}{4 π ε _{0} L ^{2}}

(B)

\frac{Q}{3 π ε _{0} L ^{2}}

(C)

\frac{Q}{2 3 π ε _{0} L ^{2}}

(D)

\frac{Q}{4 π ε _{0} L ^{2}}

JEE Main 2021

LEVELJEE Advanced

A cube of side $a$ has point charges $+ Q$ located at each of its vertices except at the origin, where the charge is $- Q$ . The electric field at the centre of cube is

(A)

\frac{- Q}{3 3 π ε _{0} a ^{2}} (\overset{x}{^} + \overset{y}{^} + \overset{z}{^})

(B)

\frac{Q}{3 3 π ε _{0} a ^{2}} (\overset{x}{^} + \overset{y}{^} + \overset{z}{^})

(C)

\frac{- 2 Q}{3 3 π ε _{0} a ^{2}} (\overset{x}{^} + \overset{y}{^} + \overset{z}{^})

(D)

\frac{2 Q}{3 3 π ε _{0} a ^{2}} (\overset{x}{^} + \overset{y}{^} + \overset{z}{^})

JEE Main 2021

LEVELJEE Main

What will be the magnitude of electric field at point $O$ as shown in figure? Each side of the figure is $l$ and perpendicular to each other.

(A)

\frac{1}{4 π ε _{0}} \frac{q}{l ^{2}}

(B)

\frac{1}{4 π ε _{0}} \frac{q}{l ^{2}} (22 - 1)

(C)

\frac{q}{4 π ε _{0} ( 2 l ) ^{2}}

(D)

\frac{1}{4 π ε _{0}} \frac{q}{l ^{2}} (2)

JEE Main 2020

LEVELJEE Main

Charges $Q_{1}$ and $Q_{2}$ are at points $A$ and $B$ of a right angle triangle $O A B$ (see figure). The resultant electric field at point $O$ is perpendicular to the hypotenuse, then $Q_{1} / Q_{2}$ is proportional to

(A)

\frac{x _{1}^{3}}{x _{2}^{3}}

(B)

\frac{x _{2}}{x _{1}}

(C)

\frac{x _{1}}{x _{2}}

(D)

\frac{x _{2}^{2}}{x _{1}^{2}}

JEE Main 2019

LEVELJEE Main

The bob of a simple pendulum has mass $2 g$ and a charge of $5.0 μ C$ . It is at rest in a uniform horizontal electric field of intensity $2000 V/m$ . At equilibrium, the angle that the pendulum makes with the vertical is (take $g = 10 m/s^{2}$ )

(A)

tan^{- 1} (2.0)

(B)

tan^{- 1} (0.2)

(C)

tan^{- 1} (5.0)

(D)

tan^{- 1} (0.5)

JEE Main 2020

LEVELJEE Advanced

A charged particle (mass $m$ and charge $q$ ) moves along X-axis with velocity $v_{0}$ . When it passes through the origin it enters a region having uniform electric field $E = - E \hat{j}$ which extends upto $x = d$ . Equation of path of electron in the region ( $x > d$ ) is

(A)

y = \frac{q E d}{m v _{0}^{2}} x

(B)

y = \frac{q E d}{m v _{0}^{2}} (x - d)

(C)

y = \frac{q E d}{m v _{0}^{2}} (\frac{d}{2} - x)

(D)

y = \frac{q E d ^{2}}{m v _{0}^{2}} x

JEE Main 2020

LEVELJEE Main

Three charged particles $A, B$ and $C$ with charges $- 4 q, 2 q$ and $- 2 q$ are present on the circumference of a circle of radius $d$ . The charged particles $A, C$ and centre $O$ of the circle formed an equilateral triangle as shown in figure. Electric field at $O$ along x-direction is

(A)

\frac{2 3 q}{π ε _{0} d ^{2}}

(B)

\frac{3 q}{4 π ε _{0} d ^{2}}

(C)

\frac{3 3 q}{4 π ε _{0} d ^{2}}

(D)

\frac{3 q}{π ε _{0} d ^{2}}

JEE Main 2021

LEVELJEE Main

A body having specific charge $8 μ C/g$ is resting on a frictionless plane at a distance $10 cm$ from the wall (as shown in the figure). It starts moving towards the wall when a uniform electric field of $100 V/m$ is applied horizontally towards the wall. If the collision of the body with the wall is perfectly elastic, then the time period of the motion will be ...... s.

LEVELJEE Main

Two point charges $+ 8 q$ and $- 2 q$ are located at $x = 0$ and $x = L$ , respectively. The location of a point on the x-axis at which the net electric field due to these two point charges is zero, is

(A)

2 L

(B)

\frac{L}{4}

(C)

8 L

(D)

4 L

JEE Main 2019

LEVELJEE Advanced

Two point charges $q_{1} (10 μ C)$ and $q_{2} (- 25 μ C)$ are placed on the x-axis at $x = 1 m$ and $x = 4 m$ , respectively. The electric field (in V/m) at a point $y = 3 m$ on Y-axis is $(Take, \frac{1}{4 π ϵ _{0}} = 9 \times 1 0^{9} N-m^{2} C^{- 2})$

(A)

(63 \hat{i} - 27 \hat{j}) \times 1 0^{2}

(B)

(81 \hat{i} - 81 \hat{j}) \times 1 0^{2}

(C)

(- 81 \hat{i} + 81 \hat{j}) \times 1 0^{2}

(D)

(- 63 \hat{i} + 27 \hat{j}) \times 1 0^{2}

JEE Main 2020

LEVELJEE Main

A small point mass carrying some positive charge on it, is released from the edge of a table. There is an 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)

A thin semi-circular ring of radius $r$ has a positive charge $q$ distributed uniformly over it. The net field $E$ at the centre $O$ is

(A)

\frac{q}{4 π ^{2} ε _{0} r ^{2}} \hat{j}

(B)

- \frac{q}{4 π ^{2} ε _{0} r ^{2}} \hat{j}

(C)

- \frac{q}{2 π ^{2} ε _{0} r ^{2}} \hat{j}

(D)

\frac{q}{2 π ^{2} ε _{0} r ^{2}} \hat{j}

JEE Main 2020

LEVELJEE Main

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)

A charged oil drop is suspended in uniform field of $3 \times 1 0^{4} Vm^{- 1}$ so that it neither falls nor rises. The charge on the drop will be (take the mass of the charge $= 9.9 \times 1 0^{- 15} kg$ and $g = 10 ms^{- 2}$ )

(A)

3.3 \times 1 0^{- 18} C

(B)

3.2 \times 1 0^{- 18} C

(C)

1.6 \times 1 0^{- 18} C

(D)

4.8 \times 1 0^{- 18} C

JEE Main 2019

LEVELJEE Advanced

Four point charges $- q, + q, + q$ and $- q$ are placed on Y-axis at $y = - 2 d$ , $y = - d$ , $y = + d$ and $y = + 2 d$ , respectively. The magnitude of the electric field $E$ at a point on the X-axis at $x = D$ , with $D >> d$ , will behave as

(A)

E \propto \frac{1}{D}

(B)

E \propto \frac{1}{D ^{3}}

(C)

E \propto \frac{1}{D ^{2}}

(D)

E \propto \frac{1}{D ^{4}}

JEE Main 2019

LEVELJEE Advanced

A positive point charge is released from rest at a distance $r_{0}$ from a positive line charge with uniform density. The speed ( $v$ ) of the point charge, as a function of instantaneous distance $r$ from line charge, is proportional to

(A)

v \propto (\frac{r}{r _{0}})

(B)

v \propto e^{+ \frac{r}{r _{0}}}

(C)

v \propto ln (\frac{r}{r _{0}})

(D)

v \propto ln (\frac{r}{r _{0}})

JEE Advanced 2018

LEVELJEE Advanced

The electric field $E$ is measured at a point $P (0, 0, d)$ generated due to various charge distributions and the dependence of $E$ on $d$ is found to be different for different charge distributions. Column I contains different relations between $E$ and $d$ . Column II describes different electric charge distributions, along with their locations. Match the functions in Column I with the related charge distributions in Column II. Column I A. $E$ is independent of $d$ B. $E \propto \frac{1}{d}$ C. $E \propto \frac{1}{d ^{2}}$ D. $E \propto \frac{1}{d ^{3}}$ Column II p. A point charge $Q$ at the origin q. A small dipole with point charges $Q$ at $(0, 0, l)$ and $- Q$ at $(0, 0, - l)$ . (Take, $2 l ≪ d$ ) r. An infinite line charge coincident with the $X$ -axis, with uniform linear charge density $λ$ . s. Two infinite wires carrying a uniform linear charge density parallel to the $X$ -axis. The one along $(y = 0, z = l)$ has a charge density $+ λ$ and the one along $(y = 0, z = - l)$ has a charge density $- λ$ . (Take, $2 l ≪ d$ ). t. Infinite plane charge coincident with the $x y$ -plane with uniform surface charge density.

(A)

\to

t; B

\to

r, s; C

\to

p; D

\to

(B)

\to

t; B

\to

r; C

\to

p, s; D

\to

(C)

\to

t; B

\to

r; C

\to

p, q; D

\to

(D)

\to

s; B

\to

q, r; C

\to

p; D

\to

JEE Advanced 2019

LEVELJEE Main

A particle of mass $1 0^{- 3} kg$ and charge $1.0 C$ is initially at rest. At time $t = 0$ , the particle comes under the influence of an electric field $E (t) = E_{0} sin ω t \hat{i}$ , where $E_{0} = 1.0 N C^{- 1}$ and $ω = 1 0^{3} rad s^{- 1}$ . Consider the effect of only the electrical force on the particle. Then, the maximum speed in $m s^{- 1}$ , attained by the particle at subsequent times is ......

LEVELJEE Main

A pendulum bob of mass 80 mg and carrying a charge of $2 \times 1 0^{- 8} C$ is at rest in a horizontal uniform electric field of 20,000 V/m. Find the tension in the thread of the pendulum and the angle it makes with the vertical. (Take $g = 9.8 ms^{- 2}$ )

LEVELJEE Main

Six charges, three positive and three negative of equal magnitude are to be placed at the vertices of a regular hexagon such that the electric field at $O$ is double the electric field when only one positive charge of same magnitude is placed at $R$ . Which of the following arrangements of charge is possible for, $P, Q, R, S, T$ and $U$ respectively?

(A)

+, -, +, -, -, +

(B)

+, -, +, -, +, -

(C)

+, +, -, +, -, -

(D)

-, +, +, -, +, -

JEE Main 2012

LEVELJEE Main

Two large vertical and parallel metal plates having a separation of $1 cm$ are connected to a DC voltage source of potential difference $X$ . A proton is released at rest midway between the two plates. It is found to move at $4 5^{\circ}$ to the vertical just after release. Then $X$ is nearly

(A)

1 \times 1 0^{- 5} V

(B)

1 \times 1 0^{- 7} V

(C)

1 \times 1 0^{- 9} V

(D)

1 \times 1 0^{- 10} V

JEE Advanced 1998

LEVELJEE Advanced

A positively charged thin metal ring of radius $R$ is fixed in the $x$ - $y$ plane with its centre at the origin $O$ . A negatively charged particle $P$ is released from rest at the point $(0, 0, z_{0})$ where $z_{0} > 0$ . Then the motion of $P$ is

* Multiple Correct Options

(A)

periodic for all values of

z_{0}

satisfying

0 < z_{0} < \infty

(B)

simple harmonic for all values of

z_{0}

satisfying

0 < z_{0} \leq R

(C)

approximately simple harmonic provided

z_{0} ≪ R

(D)

such that

P

crosses

O

and continues to move along the negative

z

-axis towards

z = - \infty

JEE Advanced 2015

LEVELJEE Advanced

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 is/are

(A)

both charges execute simple harmonic motion.

(B)

both charges will continue moving in the direction of their displacement.

(C)

charge

+ q

executes simple harmonic motion while charge

- q

continues moving in the direction of its displacement.

(D)

charge

- q

executes simple harmonic motion while charge

+ q

continues moving in the direction of its displacement.

JEE Advanced 2014

LEVELJEE Main

Charges $Q, 2 Q$ and $4 Q$ are uniformly distributed in three dielectric solid spheres 1, 2 and 3 of radii $R /2, R$ and $2 R$ respectively, as shown in figure. If magnitudes of the electric fields at point $P$ at a distance $R$ from the centre of spheres 1, 2 and 3 are $E_{1}, E_{2}$ and $E_{3}$ respectively, then

(A)

E_{1} > E_{2} > E_{3}

(B)

E_{3} > E_{1} > E_{2}

(C)

E_{2} > E_{1} > E_{3}

(D)

E_{3} > E_{2} > E_{1}

JEE Advanced 2013

LEVELJEE Advanced

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 centre of the spheres, is zero. The ratio $ρ_{1} / ρ_{2}$ can be

* Multiple Correct Options

(A)

- 4

(B)

- \frac{32}{25}

(C)

\frac{32}{25}

(D)

4

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A cube of side a has point charges +Q located at each of its vertices except at the origin, where the charge is −Q. The electric field at the centre of cube is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } What will be the magnitude of electric field at point O as shown in figure? Each side of the figure is l and perpendicular to each other.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A thin semi-circular ring of radius r has a positive charge q distributed uniformly over it. The net field E at the centre O is

A cube of side $a$ has point charges $+ Q$ located at each of its vertices except at the origin, where the charge is $- Q$ . The electric field at the centre of cube is

What will be the magnitude of electric field at point $O$ as shown in figure? Each side of the figure is $l$ and perpendicular to each other.

A thin semi-circular ring of radius $r$ has a positive charge $q$ distributed uniformly over it. The net field $E$ at the centre $O$ is