Electric Field

Q. Calculate the electric field Intensity at any point an electric dipole.

Q. A particle of charge $q$ and mass $m$ moves rectilinearly under the action of an electric field $E=\alpha -\beta x$. Here, $\alpha$ and $\beta$ are positive constants and $x$ is the distance from the point where the particle was initially at rest. Then,

1. The motion of the particle is oscillatory
2. The amplitude of the particle is $\left(\frac{\alpha }{\beta }\right)$
3. The mean position of the particle is at $x=\left(\frac{\alpha }{\beta }\right)$
4. The maximum acceleration of the particle is $\frac{q\alpha }{m}$

Q.

A point charge produces an electric field of magnitude $5.0{\text{NC}}^{-1}$ at a distance of 40 cm from it. What is the magnitude of charge?

1. $8.9\text{C}$

2. $8.9\times {10}^{-11}\text{C}$

3. $-8.9\times {10}^{11}\text{C}$

4. ${10}^{-11}\text{C}$

Q.

Find electric field at point (2, 1) due to an electron placed at the origin

1. $\overrightarrow{E}=\frac{1.44\times {10}^{-9}}{25}(-2\hat{i}-\hat{j})$

2. $\overrightarrow{E}=\frac{1.44\times {10}^{-9}}{5\sqrt{5}}(2\hat{i}+\hat{j})$

3. $\overrightarrow{E}=\frac{1.44\times {10}^{-9}}{5\sqrt{5}}(-2\hat{i}-\hat{j})$

4. $\overrightarrow{E}=\frac{1.44\times {10}^{-9}}{25}(\hat{i}+2\hat{j})$

Q.

Three infinite long plane sheets carrying uniform charge densities
${\sigma }_1=-\sigma ,{\sigma }_2=+2\sigma$ and ${\sigma }_3=+3\sigma$ are placed parallel to the x-z plane at y =a, y=3a and y=4a as shown in Fig. 20.18. The electric field at point P is

1. zero

2. $-\frac{2\sigma }{{ϵ}_0}\hat{j}$

3. $-\frac{3\sigma }{{ϵ}_0}\hat{j}$

4. $\frac{3\sigma }{{ϵ}_0}\hat{j}$

Q. A rod AB of length $L$ and mass $m$ is uniformly charged with a charge Q and it is suspended from end A as shown in the figure. The rod can freely rotate about A in the plane of figure. An electric field $E$ is suddenly switched on in the horizontal direction due to which rod gets turned by a maximum angle ${90}^o$. The magnitude of E is equal to $\frac{nmg}{Q}$. Find the value of n.

Q. The intensity of the electric field required to keep a water drop of radius ${10}^{-5}$ cm, just suspended in air when charged with one electron is approximately (g = 10newton / kg, e$=1.6\times {10}^{-19}$ coulomb)

1. 260 volt / cm
2. 260 newton / coulomb
3. 130 volt / cm
4. 130 newton / coulomb

Q. Find the electric field at a point O.

1. Zero
2. $2\sqrt{2}\frac{kq}{a^2}$
3. $3\sqrt{2}\frac{kq}{a^2}$
4. $\frac{kq}{a^2}$

Q.

The electric field in a region is given by
$E=(2\hat{i}+3\hat{j})\times {10}^{3}N{C}^{-1}$
The electric flux through a rectangular surface $10cm\times 20cm$ held parallel to the y-z plance is

1. $40N{C}^{-1}{m}^2$

2. $50N{C}^{-1}{m}^2$

3. $60N{C}^{-1}{m}^2$

4. zero

Q. $1\mu \text{C}$ charge is uniformly distributed on a spherical shell given by equation $x^2+y^2+z^2=25$. What will be the flux through an imaginary sphere of radius $3\text{m}$ and centre at origin ?

1. $5{\text{N-m}}^2/\text{C}$
2. $50{\text{N-m}}^2/\text{C}$
3. Zero
4. $25{\text{N-m}}^2/\text{C}$

Q. In LC OSCILLATION maximum charge on capacitor can be Q.if at any instant , electric energy and magnetic energy associated with circit is equal , then charge on capacitor at that instant is

Q. A graph of the $\text{x-}$component of the electric field as a function of $x$ in a region of space is shown. The $\text{y}$ and $\text{z}$ components of the electric field are zero in this region. If the electric potential is $10\text{V}$ at the origin, then potential at $x=2\text{m}$ is

1. $40\text{V}$
2. $30\text{V}$
3. $-10\text{V}$
4. $10\text{V}$

Q. A charge particle enters normally inside an external uniform magnetic field region of width d as shown. The magnitude of magnetic field is B. Time after which it comes out of this magnetic field will be

एक आवेश कण दर्शाए अनुसार d चौड़ाई के एक बाह्य एकसमान चुम्बकीय क्षेत्र के अन्दर लम्बवत् रूप से प्रवेश करता है। चुम्बकीय क्षेत्र का परिमाण B है। तब यह कितने समय के बाद इस चुम्बकीय क्षेत्र से बाहर आएगा?

1. $\frac{\pi m}{qB}$
2. $\frac{2\pi m}{3qB}$
3. $\frac{2\pi m}{qB}$
4. $\frac{\pi m}{3qB}$

Q. The variation of potential with distance $r$ from a fixed point is shown in Figure. The electric field at $r=5\text{cm}$, is :

Q. A toy car with charge $q$ moves on a frictionless horizontal plane surface under the influence of a uniform electric field $\overrightarrow{E}$. Due to the force $q$$\overrightarrow{E}$, its velocity increases from $0m/s$ to $6m/s$ in one second. At that instant the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between $0$ to $3$ seconds are respectively

1. $2m/s,4m/s$
2. $1m/s,3m/s$
3. $1m/s,3.5m/s$
4. $1.5m/s,3m/s$

Q.

An electron is fixed at the origin as shown. What is the electric field at $\text{A}$?
(The coordinates are in metre)

1. $3.6\times {10}^{-19}\text{N/C}\hat{i}$
2. $-3.6\times {10}^{-10}\text{N/C}\hat{i}$
3. $3.6\times {10}^{-10}\text{N/C}\hat{i}$
4. None of these

Q. Find the electric field at the symmetric centre. There is no charge at point P.

1. $\frac{kq}{a^2}$
2. $2\frac{kq}{a^2}$
3. $3\frac{kq}{a^2}$
4. $2\sqrt{2}\frac{kq}{a^2}$

Q. A uniform force of $(3\hat{i}+\hat{j})\text{N}$ acts on a particle of mass $2\text{kg}.$ Hence the particle is displaced from position $(2\hat{i}+\hat{k})\text{m}$ to position $(4\hat{i}+3\hat{j}-\hat{k})\text{m}.$ The work done by the force on the particle is -

1. $15\text{J}$
2. $6\text{J}$
3. $13\text{J}$
4. $9\text{J}$

Q. A vertical electric field of magnitude $4\times {10}^5\text{N/C}$ just prevents a water droplet of mass $1\times {10}^{-4}\text{kg}$ from falling. Find the charge on the droplet.

1. $4.5\times {10}^{-9}\text{C}$
2. $2.5\times {10}^{-9}\text{C}$
3. $3.5\times {10}^{-9}\text{C}$
4. $1.5\times {10}^{-9}\text{C}$

Q. A circular disc of mass 10 kg is suspended by a wire attached to its centre. The wire is twisted by rotating the disc and released. The period of torsional oscillation is found to be 1.5 s. The radius of the disc is 15 cm. Determine the torsional spring constant of the wire. (Torsional spring constant $\alpha$ is defined by the relation $J=-\alpha \theta$, where J is the restoring couple and $\theta$ the angle of twist).

Q. What is gravitational potential and why is it a scalar quantity if electric field is a vector quantity? Also are constants of proportionality necessarily scalars? If not then why is coefficient of friction a scalar?

Q. A point object having charge $q$ and mass $m$ kept on the top of a frictionless and insulated hemisphere. When a horizontal electric field is applied, the object starts sliding down and loses contact from the surface at an angle $\theta =si{n}^{-1}\frac{3}{5}$ from the vertical. The ratio of force of gravity and the force due to interaction with the field acting on this object is

1. $\frac{9}{2}$
2. $\frac{7}{2}$
3. $\frac{9}{7}$
4. $\frac{7}{5}$

Q. The electric field in a region is given by $\overrightarrow{E}=(1200\hat{i}+1600\hat{j})\text{N/C}$. Find the flux of this field through a rectangular surface of area $0.2{\text{m}}^2$ parallel to the $y-z$ plane.

1. $140{\text{N-m}}^2/\text{C}$
2. $240{\text{N-m}}^2/\text{C}$
3. $340{\text{N-m}}^2/\text{C}$
4. $440{\text{N-m}}^2/\text{C}$

Q. $1\mu \text{C}$ charge is uniformly distributed on a spherical shell given by equation $x^2+y^2+z^2=25$. What will be the flux through an imaginary sphere of radius $3\text{m}$ and centre at origin ?

1. Zero
2. $50{\text{N-m}}^2/\text{C}$
3. $5{\text{N-m}}^2/\text{C}$
4. $25{\text{N-m}}^2/\text{C}$

Q. There is a uniform electric field of strength ${10}^3$ V/m along y-axis. A body of mass 1g and charge ${10}^{-6}$C is projected into the field from origin along the positive x-axis with a velocity 10m/s. Its speed in m/s after 10s is (Neglect gravitation)

1. 10
2. $5\sqrt{2}$
3. $10\sqrt{2}$
4. 20

Q.

One can add electric field and gravitational field.

1. True

2. False

Q. When a negative charge is taken at a height from earth's surface, then its potential energy

1. Decreases
2. Increases
3. Remains unchanged
4. Will become infinity

Q. There is charge $Q$ placed at a point in space. The fields at two points which are equidistant from the charge are always equal in magnitude and direction.

1. False
2. True

Q. The variation of potential $V$ with distance $r$ from a fixed point is shown in the figure. The magnitude of electric field at $r=2\text{cm}$ is

1. $200\text{V/m}$
2. $100\text{V/cm}$
3. $100\text{V/m}$
4. $200\text{V/cm}$

Q. electrical force acting between two charges q1 and q2 having a separation r is given by F=K q1q2/r² obtain dimension of k.