Magnetic Field Due to a Circular Ring on the Axis

Q. A disc of radius $R$ uniformly charged with a charge $Q$ is rotated at angular velocity ${}^{\prime }{\omega }^{\prime }$ about an axis passing through its center and perpendicular to plane disc. Net magnetic field at center of disc is.

1. $\frac{{\mu }_0}{u}\frac{Q\omega }{R}$
2. $\frac{{\mu }_{0}Q\omega }{4\pi R}$
3. $\frac{{\mu }_{0}Q\omega }{2\pi R}$
4. $\frac{{\mu }_{0}Q\omega }{2R}$

Q. A and B are concentric circular conductors with center O and carrying currents $I_1$ and $I_2$ as shown in fig. The ratio of their radii is 1: 2 and ratio of their flux densities at O is 1:3 The value of $\frac{I_1}{I_2}$ is

1. $\frac{1}{6}$
2. $\frac{1}{4}$
3. $\frac{1}{2}$
4. $\frac{1}{3}$

Q. A conductor of length l has shape of a semicylinder of radius R(<<l). Crossection of the conductor is shown in figure. Thickness of conductor is t(<<R) and conductivity of its material is $\delta ={\delta }_{0}cos\theta$. If an ideal battery of emf V is connected across its end faces, then magnetic field at point O on the axis of semicylinder is $n\frac{{\mu }_0{\delta }_{0}Vt}{l}$. Here, n is

Q. A and B are concentric circular conductors with center O and carrying currents $I_1$ and $I_2$ as shown in fig. The ratio of their radii is 1: 2 and ratio of their flux densities at O is 1:3 The value of $\frac{I_1}{I_2}$ is

1. $\frac{1}{6}$
2. $\frac{1}{4}$
3. $\frac{1}{2}$
4. $\frac{1}{3}$

Q. Two identical thin rings, each of radius $R$, are coaxially placed a distance $R$ apart . If $Q_1$ and $Q_2$ are respectively the charges uniformly spread on the two rings, the work done in moving a charge $q$ from the centre of one ring to that of the other is equal to

1. $\frac{q(Q_1-Q_2)(\sqrt{2}+1)}{\sqrt{2}\left(4\pi {\epsilon }_{0}R\right)}$
2. $\frac{q(Q_1-Q_2)(\sqrt{2}-1)}{\sqrt{2}\left(4\pi {\epsilon }_{0}R\right)}$
3. Zero
4. $\frac{q(Q_1+Q_2)(\sqrt{2}-1)}{\sqrt{2}\left(4\pi {\epsilon }_{0}R\right)}$

Q.

A circular current carrying coil has a radius R. The distance from the centre of the coil on the axis where the magnetic induction will be ${\frac{1}{8}}^{th}$ to its value at the centre of the coil, is

1. $\frac{R}{\sqrt{3}}$

2. $R\sqrt{3}$

3. $2\sqrt{3}R$

4. $\frac{2}{\sqrt{3}}R$