Magnetic Field Due to a Circular Ring on the Axis

Q. A direct current is passing through a wire. It is bent to form a coil of one turn. Now, it is further bent into a coil of $4$ turns but of smaller radius. The ratio of magnetic induction at the centre of this to the magnetic induction at the centre of coil of one turn is

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

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

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 coil having N turns is wound tightly in the form of a spiral with inner and outer radii 'a' and 'b' respectively. When a current I passes through the coil, the magnetic field at the centre is

1. $\frac{{\mu }_{0}NI}{b}$
   
2. $\frac{2{\mu }_{0}NI}{a}$
   
3. $\frac{{\mu }_{0}NI}{2(b-a)}ln\frac{b}{a}$
   
4. $\frac{{\mu }_0{I}^N}{2(b-a)}ln\frac{b}{a}$

Q.

Find the magnetic induction of the field at the point O of a loop with current I, whose shape is illustrated in the figure.

1. $\frac{{\mu }_{0}I}{3\pi }(\frac{3\pi }{2a}+\frac{\sqrt{2}}{b})$

2. $\frac{{\mu }_{0}I}{2\pi }(\frac{3\pi }{4a}+\frac{\sqrt{2}}{2b})$

3. $\frac{{\mu }_{0}I}{2\pi }(\frac{2\pi }{3a}+\frac{\sqrt{2}}{b})$

4. $\frac{{\mu }_{0}I}{2\pi }(\frac{3\pi }{4a}+\frac{\sqrt{2}}{2b})$

Q. A straight wire of length $\left({\pi }^2\right)$ metre is carrying a current of 2A and the magnetic field due to it is measured at a point distant 1 cm from it. If the wire is to be bent into a circle and is to carry the same current as before, the ratio of the magnetic field at its centre to that obtained in the first case would be

1. 1 : 50
2. 50 : 1
3. 100 : 1
4. 1 : 100

Q. An infinitely long straight conductor is bent into the shape as shown in the figure. It carries a current of i ampere and the radius of the circular loop is r metre. Then the magnetic induction at its centre will be

1. Infinite
2. 
3. 
4. Zero

Q. Two wires are wound into coils of one turn and three turns of equal radius. If the same current is passed through the coils, the ratio of magnetic field at their centres will be:

1. 1:4
2. 1:9
3. 9:1
4. 1:3

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 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