Electric Field Due to a Dipole at a General Point in Space

Q. A dipole with an electric moment p is located at a distance r from a Long thread charged uniformaly with a linear charge density lambda. Find the force F acting on the dipole if the vector p is oriented along the thread

Q. Two point charges $q_1\left(\sqrt{10}\mu \text{C}\right)$ and $q_2(-25\mu \text{C})$ are placed on the x-axis at $x=1\text{m}$ and $x=4\text{m}$ respectively.The electric field in $\left(\text{V/m}\right)$ at a point $y=3\text{m}$ on $y-$axis is

$[\text{Take}\frac{1}{4\pi {\epsilon }_0}=9\times {10}^9{\text{Nm}}^2{\text{C}}^{-2}]$

1. $(63\hat{j}-27\hat{i})\times {10}^2$
2. $(-81\hat{i}+81\hat{j})\times {10}^2$
3. $(63\hat{i}-27\hat{j})\times {10}^2$
4. $(81\hat{i}-81\hat{j})\times {10}^2$

Q. The electric field due to a dipole at a distance r on its axis is

1. Inversely proportional to $r^3$
2. Directly proportional to $r^3$
3. Directly proportional to $r^2$
4. Inversely proportional to $r^2$

Q. A square of side $L$ is in the plane of the paper. A uniform electric field $E$, also in the plane of the paper, is limited only to the lower half of the square surface as shown in the figure. The electric flux (in SI unit) associated with the surface is

1. $2E{L}^2$
2. $3E{L}^2$
3. Zero
4. $E{L}^2$

Q. The three charges $\frac{q}{2},q$ and $\frac{q}{2}$ are placed at the corners $A,B\text{and}C$ of a square of side 'a' as shown in figure. The magnitude of electric field $\left(E\right)$ at the corner $D$ of the square is

1. $\frac{q}{4\pi {ϵ}_0{a}^2}(1-\frac{1}{\sqrt{2}})$
2. $\frac{q}{4\pi {ϵ}_0{a}^2}(\frac{1}{\sqrt{2}}+\frac{1}{2})$
3. $\frac{q}{4\pi {ϵ}_0{a}^2}(\frac{1}{\sqrt{2}}-\frac{1}{2})$
4. $\frac{q}{4\pi {ϵ}_0{a}^2}(1+\frac{1}{\sqrt{2}})$

Q. A uniform electric field $E$ is parallel to the axis of a hollow hemisphere of radius $r$. The electric flux through the hemispherical surface is

1. $4\pi r^{2}E$
2. $\frac{3}{8}\pi r^{2}E$
3. $\pi r^{2}E$
4. $2\pi r^{2}E$

Q. A concentric spherical cavity is cut out from a solid conducting sphere and a charge $+Q$ is placed at the centre of the cavity. The magnitude of net electric field $E$ and net potential $V$ at point $A$ is
[$k=\frac{1}{4\pi {ϵ}_0}$]

1. $E=\frac{4kQ}{R^2},V=\frac{3kQ}{2R}$
2. $E=\frac{kQ}{R^2},V=0$
3. $E=\frac{4kQ}{R^2},V=\frac{kQ}{R}$
4. $E=\frac{kQ}{4R^2},V=\frac{kQ}{2R}$

Q.

A half ring of radius R is charged with a linear charged density $\lambda$. The field at the centre is

1. 0

2. $\frac{k\lambda }{R}$

3. $\frac{2k\lambda }{R}$

4. $\frac{k\pi \lambda }{R}$

Q. Through which of the spheres, net electric flux is zero?

1. 
2. 
3. 
4. 

Q. Find the flux through the surface $\left(APB\right)$ of the given Gaussian surface containing a point charge $+9\text{nC}$ as shown in figure.
[$ABC$ is an equilateral triangle and take ${ϵ}_o=9\times {10}^{-12}{\text{C}}^2/{\text{N-m}}^2$]

1. $633{\text{N-m}}^2\text{/C}$
2. $733{\text{N-m}}^2\text{/C}$
3. $833{\text{N-m}}^2\text{/C}$
4. $933{\text{N-m}}^2\text{/C}$

Q.

A strong magnetic field is applied to a stationary electron. Then the electron remains ____________.

Q.

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?

1. The electric flux passing through the curved surface of the hemisphere is $-\frac{Q}{2{\in }_0}(1-\frac{1}{\sqrt{2}})$

2. The component of the electric field normal to the flat surface is constant over the surface

3. Total flux through the curved and the flat surface is $\frac{Q}{{\in }_0}$

4. The circumference of the flat surface is an equipotential

Q. If a dipole of dipole moment p^ i is placed at point (0, y) anda point charge at the origin of a co-ordinate system, netelectric field at point (x, x + y) vanishes. If x and y both arepositive, the co-ordinate y is equal to

Q. An imaginary truncated cone is placed in uniform electric field E as shown in the figure. Then total flux linked with cone is

एक काल्पनिक रूंडित शंकु को एकसमान विद्युत क्षेत्र E में चित्रानुसार रखा जाता है, तब शंकु से सम्बद्ध कुल फ्लक्स है

1. Positive
   
   धनात्मक
2. Negative
   
   ऋणात्मक
3. Zero
   
   शून्य
4. Non-zero
   
   अ-शून्य

Q. The distance between the two charges +q and -q of a dipole is r. On the axial line at a distance d from the centre of dipole, the intensity is proportional to

1. $\frac{q}{d^2}$
2. $\frac{qr}{d^2}$
3. $\frac{q}{d^3}$
4. $\frac{qr}{d^3}$

Q. Charge $Q,2Q$ and $-Q$ are given to three concentric conducting spherical shells $A,B$ and $C$ respectively as shown in figure. The ratio of charges on the inner and outer surfaces of shell $C$ will be

1. $+\frac{3}{4}$
2. $\frac{-3}{4}$
3. $\frac{3}{2}$
4. $\frac{-3}{2}$

Q.

In a non uniform external field the dipole has a net force in the anti- parallel direction of increasing field when

1. 

2. 

3. 

4. none of these

Q. A short electric dipole has dipole moment of $3\sqrt{2}\times {10}^{-10}\text{C m}$. The electric potential due to the dipole at a point which is at a distance $0.3\text{m}$ from the centre of the dipole, situated on a line making an angle of ${45}^{\circ }$ with the dipole axis is $(\frac{1}{4\pi {ϵ}_0}=9\times {10}^9{\text{N m}}^2/{\text{C}}^2)$ :

1. $300\text{V}$
2. $30\text{V}$
3. $200\text{V}$
4. $20\text{V}$

Q.

A charge +q is placed at the middle of a closed cylinder of radius r and height h. A spherical shell of radius r with its centre at the point at which charge is placed, is so oriented so that h > 2 r. what is the ratio of flux passing thorugh cylinder and sphere?

1. $\frac{(2r+h)}{2r}$

2. $\frac{1}{4}$

3. $\frac{h}{2r}$

4. $\frac{1}{1}$

Q.

The ratio of electric field at a point A and at point B due to the uniformly charged spherical conductor as shown, is

1. 2:5

2. 1:3

3. 0

4. 1:1

Q. What is the difference between AMPERES MAXWELL CIRCUITAL LAW and the AMPERES MAXWELL LAW ?

Q. A charge $q$ is distributed uniformly on the surface of a solid sphere of radius $R$. It is covered by a concentric hollow conducting sphere of radius $2R$. The charge on outer surface of hollow sphere if it is earthed is

1. $q$
2. $-q$
3. $0$
4. $2q$

Q. Find the flux of the electric field through a spherical surface of radius R due to a charge of 10⁻⁷ C at the centre and another equal charge at a point 2R away from the centre (figure 30-E2).

Q. The distance between charges $5\times {10}^{-11}C$ is 0.2m. The distance at which a third charge should be placed in order that it will not experience any force along the line joining the two charges is (the distance from smaller charge)

1. 0.4 m towards the larger charge
2. 0.6 m on the other side
3. 0.5 m on the other side
4. 0.3 m to wards larger charge

Q. An electric dipole of moment $\overrightarrow{p}$ is placed at the origin along the x-axis. The angle made by electric field with x-axis at a point P, whose position vector makes an angle $\theta$ with x-axis, is ( where $\tan \alpha =\frac{1}{2}\tan \theta$)

1. $\alpha$
2. $\theta$
3. $\theta +\alpha$
4. $\theta +2\alpha$

Q. Two large conducting plates are placed parallel to each other and they carry equal and opposite charges with surface density $\sigma$ as shown in the figure (30-E6). Find the electric field (a) at the left of the plates (b) in between the plates and (c) at the right of the plates.

Q. An electric dipole is placed at the centre of a sphere. Select the correct option. (More than one option may be correct)

1. The flux of the electric field through the sphere is zero
2. The electric field is zero at every point of the sphere
3. The electric field is zero on a circle on the sphere
4. The electric field is not zero anywhere on the sphere

Q. The electric field due to an electric dipole at a distance $r$ from its center in axial position is $E.$ If the dipole is rotated through an angle of ${90}^o$ about its perpendicular axis, the electric field at the same point will be

1. $E$
2. $\frac{E}{2}$
3. $\frac{E}{4}$
4. $2E$

Q. The force between two short electric dipole placed on the same axis at a distance R, varies as?

1. $R^{-1}$
2. $R^{-2}$
3. $R^{-3}$
4. $R^{-4}$

Q. An electric dipole is placed at the origin and is directed along the x-axis. At a point P, far away from the dipole, the electric field is parallel to the y-axis. OP makes an angle $\theta$ with the x-axis. Then,

1. $\tan \theta =\sqrt{2}$
2. $\tan \theta =1$
3. $\tan \theta =\frac{1}{\sqrt{2}}$
4. $\tan \theta =\sqrt{3}$