Magnetic Field Due to a Circular Ring on the Axis

Q. The radius of a circular current carrying coil having a single turn is $R$. At what distance from the centre of the coil on its axis, the intensity of magnetic field will be $\frac{1}{2\sqrt{2}}$ times the intensity of magnetic field at the centre ?

Q. Field at the centre of a circular coil of radius r, through which a current I flows is

1. Directly proportional to r
2. Inversely proportional to I
3. Directly proportional to I
4. None of these.

Q. Two circular coils $X$ and $Y$, having equal number of turns and carrying equal currents in the same sense, subtend same solid angle at point $O$. If the smaller coil $X$ is midway between $O$ and $Y$ and if we represent the magnetic field due to bigger coil $Y$ at $O$ as $B_y$ and that due to smaller coil $X$ at $O$ as $B_x$, then

1. $\frac{B_y}{B_x}=1$
2. $\frac{B_y}{B_x}=2$
3. $\frac{B_y}{B_x}=\frac{1}{2}$
4. $\frac{B_y}{B_x}=\frac{1}{4}$

Q.

A charge q coulomb moves in a circle at n revolutions per second and the radius of the circle is r metre. Then magnetic field at the centre of the circle is

1. $\frac{2\mathrm{\pi q}}{nr}\times {10}^{-7}Newton/(ampere-metre)$

2. $\frac{2\mathrm{\pi q}}{r}\times {10}^{-7}Newton/(ampere-metre)$

3. $\frac{2\pi nq}{r}\times {10}^{-7}Newton/(ampere-metre)$

4. $\frac{2\mathrm{\pi q}}{r}\times {10}^{-7}Newton/(ampere-metre)$

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

Q. A thin ring of radius $r$ carries a uniformly distributed charge. The ring rotates at a constant angular speed of $n$ revolutions per second about an axis passing through centre and perpendicular to its plane. If $B$ is the magnitude of magnetic field at the centre of ring, then the charge carried by the ring is

1. $\frac{2rB}{{\mu }_{0}n}$
2. $\frac{{\mu }_{0}n}{2rB}$
3. $\frac{{\mu }_{0}n}{r}$
4. $\frac{2r}{Bq}$

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 thin ring of radius $r$ carries a uniformly distributed charge. The ring rotates at a constant angular speed of $n$ revolutions per second about an axis passing through centre and perpendicular to its plane. If $B$ is the magnitude of magnetic field at the centre of ring, then the charge carried by the ring is

1. $\frac{2rB}{{\mu }_{0}n}$
2. $\frac{{\mu }_{0}n}{2rB}$
3. $\frac{{\mu }_{0}n}{r}$
4. $\frac{2r}{Bq}$