Potential Energy of a Dipole in Uniform Electric Field

Q. A charge q is placed at the centre of the open end of cylindrical vessel. The flux of the electric field through the surface of the vessel is

1. Zero
2. $\frac{q}{2{ϵ}_0}$
3. $\frac{q}{{ϵ}_0}$
4. $\frac{2q}{{ϵ}_0}$

Q. An electric field E-(20i + 30j) N/C exists in space.If electric potential at origin is taken to be 50 Vthen electric potential at (2 m, 2 m) is(1) 10 V(3) -50 V(2) 10 V(4) 100 vyot 6o

Q. An electric charge q is placed at the centre of a cube of side $\alpha$. The electric flux on one of its faces will be

1. $\frac{q}{{ϵ}_0{a}^2}$
2. $\frac{q}{4\pi {ϵ}_0{a}^2}$
3. $\frac{q}{6{ϵ}_0}$
4. $\frac{q}{{ϵ}_0}$

Q. Two point charges of $3.2\times {10}^{-19}C$ and $-3.2\times {10}^{-19}C$ are separated from each other by $2.4\times {10}^{-10}m$.The dipole is situated in a uniform electric field of intensity $4\times {10}^{5}V{m}^{-1}.$ If the work done in rotating the dipole by ${180}^{\circ }$ is $n\times {10}^{-23}J$, the value of $n$ is . (Write upto two decimal places)

Q. An electric dipole of moment $\overrightarrow{p}$ is placed normal to the lines of force of electric intensity $\overrightarrow{E}$, then the work done in rotating it through an angle of ${180}^{\circ }$ is

1. -2pE
2. +2pE
3. pE
4. Zero

Q. An electric dipole of moment p is placed in the position of stable equilibrium in uniform electric field of intensity E. If it is rotated through an angle $\theta$ from the initial position, the potential energy of electric dipole in the final position is

1. $pEcos\theta$
2. $pEsin\theta$
3. $pE(1-cos\theta )$
4. $-pEcos\theta$

Q. A charge $Q$ is placed at a distance $a/2$ above the centre of a horizontal, square surface of edge $a$ as shown in figure. Find the flux of the electric field through the square surface.

1. $\frac{Q}{{\in }_0}$
2. $\frac{Q}{3{\in }_0}$
3. $\frac{Q}{6{\in }_0}$
4. $\frac{Q}{4{\in }_0}$

Q.

Eight dipoles of equal magnitude are placed inside a cube. The total electric flux coming out of the cube will be _____.

1. $\frac{8e}{{\epsilon }_0}$

2. $\frac{e}{{\epsilon }_0}$

3. $\frac{16e}{{\epsilon }_0}$

4. 0

Q.

What is the magnitude of the equatorial and axial fields due to a bar magnet of length 5.0 cm at a distance of 50 cm from its mid-point? The magnetic moment of the bar magnet is 0.40 Am²

Q. An electric dipole of dipole moment $\overrightarrow{p}$ is placed along a uniform electric field $\overrightarrow{E}$. The work done in rotating the dipole slowly by ${90}^{\circ }$ is

1. $2pE$
2. $pE$
3. $\sqrt{2}pE$
4. $\frac{pE}{2}$

Q. Two point charges of $3.2\times {10}^{-19}\text{C}$ and $-3.2\times {10}^{-19}\text{C}$ are seperated from each other by $2.4\times {10}^{-10}\text{m}$. The dipole is situated in a uniform electric field of intensity $4\times {10}^5\text{V/m}$. The work done in rotating the dipole by ${180}^{\circ }$ is $p\times {10}^{-24}\text{J}$. Find the value of $p$.

Q. An electric dipole consists of two chargesof 0.1 uC separated by a distance of 2.0 cm. The dipole isplaced in an external field of 10 NC. What maximumtorque does the field exert on the dipole?

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

Q. . An electric dipole has the magnitude of its charge as q and its dipole moment is p. It is placed in a uniform electric field E. If its dipole moment is along the direction of the field, the force on it and its potential energy are respectively

Q. formula for electric potential energy is U-kqq%r(2nd q represents q knot) and formula for electric potential V-kq%r why a change in both formulas?

Q. 64.A short electric dipole of dipole moment p kept in plane of a wire of linear charge density lambda as shown. The dipole makes angle 60 with local electric field. If distance of dipole from the wire is R, then force experianced by dipole is

Q. An electric dipole is placed at an angle of ${60}^{\circ }$ to a non uniform electric field. The dipole will experience

1. Torque only
2. Torque as well as net force
3. Net force only in the direction of field
4. Net force only in a direction normal to the direction of field

Q. A charge $Q$ is placed at a perpendicular distance $\frac{a}{2}$ above the centre of the horizontal, square surface of edge length $a$ as shown in figure. Find the flux of the electric field through the square surface.

1. $\frac{Q}{{\epsilon }_0}$
2. $\frac{Q}{6{\epsilon }_0}$
3. $\frac{Q}{3{\epsilon }_0}$
4. $\frac{Q}{2{\epsilon }_0}$

Q. A metallic spherical shell of inner radius $R_1$ and outer radius $R_2$ is shown in figure below. A charge is placed at the centre of the spherical cavity. The surface charge density on the inner surface is:

1. $\frac{q}{4\pi R_1^2}$
2. $\frac{-q}{4\pi R_1^2}$
3. $\frac{q^2}{4\pi R_2^2}$
4. $\frac{q}{4\pi R_2^2}$

Q. A uniform current carrying ring of mass $m$ and radius $R$ is connected by a massless string as shown in the figure. A uniform magnetic field $B_0$ exists in the region to keep the ring in horizontal position, then the current in the ring is ($l=$ length of string)

1. $\frac{mg}{\pi R{B}_0}$
2. $\frac{mg}{R{B}_0}$
3. $\frac{mg}{\pi R{B}_0}$
4. $\frac{mgl}{\pi R^2{B}_0}$

Q. $A$ and $B$ are two concentric spherical shells. If $A$ is given a charge $+q$ while $B$ is earthed as shown in figure, then

1. charge on the outer surface of shell $B$ is zero
2. the charge on $B$ is equal and opposite to that of $A$
3. the field inside $A$ and outside $B$ is zero
4. all of the above

Q. 37.Define electric dipole moment in terms of torque

Q. A capacitor $C$ is charged to a potential difference $V$ and the battery is disconnected. Now, if the capacitor plates are brought closer slowly by some distance

1. some negative work is done by external agent
2. External agent does zero work
3. Work done by external agent can be positive or negative
4. Some positive work is done by external agent

Q. A dipole of moment $\overrightarrow{p}$ is placed normal to an electric field $\overrightarrow{E}$. Work done in rotating it by an angle of $\pi$ is .

1. pE
2. +2pE
3. -2pE
4. $zero$

Q. A non-conducting disc of radius 2 $m$ is rotated about its axis of symmetry perpendicular to plane of disc with uniform angular speed $\omega$. The disc carries a charge whose density is given as $\sigma =A-Br,$ where $A$ and $B$ are positive constants and $r$ is distance from centre of the disc. The value of $\frac{A}{B}$ for which the magnetic field at the centre of the disc will be zero is

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

Q. An electric dipole of moment $p$ is lying along a uniform electric field $E$. The work done in rotating the dipole by ${90}^o$ is:

1. $pE$
2. $\sqrt{2}pE$
3. $\frac{pE}{2}$
4. $2pE$

Q. Calculate the amount of work done in turning an electric dipole of dipole moment $3\times {10}^{-8}C$-m from its position of unstable equilibrium to the position of stable equilibrium in a uniform electric field of intensity ${10}^{3}N{C}^{-1}$

Q. Assertion :A small electric dipole is moved translationally from higher potential to lower potential in uniform electric field. Work done by electric field is positive. Reason: When a positive charge is moved from higher potential to lower potential, work done by electric field is positive.

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Both Assertion and Reason are incorrect

Q. Inside a conducting spherical shell of inner radius $3R$ and outer radius $5R$ , a point charge $Q$ is placed at a distance $R$ from the centre of the shell. The electric potential at the centre of the shell will be.

1. $\frac{1}{4\pi {ϵ}_0}\frac{5Q}{6R}$
2. $\frac{1}{4\pi {ϵ}_0}\frac{13Q}{15R}$
3. $\frac{1}{4\pi {ϵ}_0}\frac{Q}{R}$
   
4. $\frac{1}{4\pi {ϵ}_0}\frac{7Q}{9R}$

Q.

Hybrid orbital with least s-character is:

1. ${\mathrm{sp}}^3\mathrm{d}$

2. ${\mathrm{sp}}^2$

3. ${\mathrm{sp}}^3$

4. $\mathrm{sp}$