Electric Potential Due to Infinite Line of Charge

Q. Two rings each of radius R have charges Q and -Q. Their axes coincide and their centres are separated by a distance R. Find the work done in moving a charge q from the centre of the first ring to the centre of the second ring.

1. $\frac{kQq}{R}$
2. zero
3. $\frac{kQq}{R}(2-\sqrt{2})$
4. $\frac{3kQq}{2R}$

Q. Determine the electric field strength vector if the potential of this field depends on $x,y$ coordinates as $V=10axy$.

1. $-10a(y\hat{i}+x\hat{j})$
2. $-a(y\hat{i}+x\hat{j})$
3. $10a(y\hat{i}+x\hat{j})$
4. $-10a(x\hat{j}+y\hat{k})$

Q. Two rings each of radius R have charges Q and -Q. Their axes coincide and their centres are separated by a distance R. Find the work done in moving a charge q from the centre of the first ring to the centre of the second ring.

1. $\frac{kQq}{R}$
2. zero
3. $\frac{kQq}{R}(2-\sqrt{2})$
4. $\frac{3kQq}{2R}$

Q. The linear charge density on a dielectric ring of radius R varies with $\theta$ as $\lambda ={\lambda }_0\cos \frac{\theta }{2},$ where ${\lambda }_0$ is a constant. Find the potential at the centre of the ring. [in volt]

Q. The arc $AB$ with the centre $C$ and the infinitely long wire having linear charge density $\lambda$ are lying in the same plane. A point charge $q_o$ moves from point $A$ to $B$ through a circular path $AB$ of radius $a$, then

1. Electric potential at $A>$ Electric potential at $B$
2. Minimum amount of work done will be $\frac{q_o\lambda }{2\pi {ϵ}_o}\ln \left(3/2\right)$
3. Minimum amount of work done will be $\frac{q_o\lambda }{2\pi {ϵ}_o}\ln \left(2/3\right)$
4. Electric potential at $A<$ Electric potential at $B$

Q. The figure shows a non-conducting ring with positive and negative charge non uniformly distributed on it such that the total charge is zero. Which of the following statements is true?

1. The potential at all the points on the axis will be zero.
2. The electric field at all the points on the axis will be zero.
3. The direction of the electric field at all points on the axis will be along the axis
4. If the ring is placed inside a uniform external electric field, then net torque and force acting on the ring would be zero.

Q. The linear charge density on a dielectric ring of radius R varies with $\theta$ as $\lambda ={\lambda }_0\cos \frac{\theta }{2},$ where ${\lambda }_0$ is a constant. Find the potential at the centre of the ring. [in volt]

Q. Find the work done by external agent in moving a $1C$ charge from point P to Q in presence of an infinitely long uniformly charged line of linear charge density $\lambda$ as shown.

1. $\frac{\lambda }{2\pi {\epsilon }_0}\ln 1.5$
2. $\frac{\lambda }{2\pi {\epsilon }_0}$
3. $\frac{\lambda }{2\pi {\epsilon }_0}\ln 5$
4. $\frac{7\lambda }{2\pi {\epsilon }_0}$

Q. The linear charge density on a dielectric ring of radius R varies with $\theta$ as $\lambda ={\lambda }_0\cos \frac{\theta }{2},$ where ${\lambda }_0$ is a constant. Find the potential at the centre of the ring. [in volt]