A galvanometer can be changed into an ammeter by using

• low resistance shunt in series

• low resistance shunt in parallel

• high resistance shunt in series

• high resistance shunt in parallel

A proton moving vertically downward enters a magnetic field pointing towards north. In which direction proton will deflect?

• East

• West

• North

• South

213.

A coil of n number of turns is wound tightly in the form of a spiral with inner and outer radii a and b respectively. When a current of strength I is passed through the coil, the magnetic field at its centre is

• $\frac{{\mathrm{\mu }}_{\mathrm{o}} \mathrm{nI}}{\left(\mathrm{b} - \mathrm{a}\right)} {\log }_{\mathrm{e}} \frac{\mathrm{a}}{\mathrm{b}}$

• $\frac{{\mathrm{\mu }}_{\mathrm{o}} \mathrm{n} \mathrm{I}}{2 \left(\mathrm{b} - \mathrm{a}\right)}$

• $\frac{2 {\mathrm{\mu }}_{\mathrm{o}} \mathrm{nI}}{\mathrm{b}}$

• $\frac{{\mathrm{\mu }}_{\mathrm{o}} \mathrm{nI}}{2 \left(\mathrm{b} - \mathrm{a}\right)} {\log }_{\mathrm{e}} \frac{\mathrm{b}}{\mathrm{a}}$

A galvanometer acting as a voltmeter should have

• low resistance in series with its coil

• low resistance in parallel with its coil

• high resistance in series with its coil

• high resistance in parallel with its coil

Magnetic field at point O will be

• $\frac{{\mathrm{\mu }}_{\mathrm{o}} \mathrm{I}}{2\mathrm{R}}$ interior

• $\frac{{\mathrm{\mu }}_{\mathrm{o}}\mathrm{I}}{2\mathrm{R}}$ exterior

• $\frac{{\mathrm{\mu }}_{\mathrm{o}} \mathrm{I}}{2\mathrm{R}}\left(1 - \frac{\mathrm{l}}{\mathrm{\pi }}\right)$ interior

• $\frac{{\mathrm{\mu }}_{\mathrm{o}}\mathrm{I}}{2\mathrm{R}} \left(1 + \frac{\mathrm{I}}{\mathrm{\pi }}\right)$ exterior

If the electric flux entering and leaving an enclosed surface respectively are ${\mathrm{\varphi }}_1 \mathrm{and} {\mathrm{\varphi }}_2$ , the electric charge inside the surface will be

• $\frac{{\mathrm{\varphi }}_2 - {\mathrm{\varphi }}_1}{{\mathrm{\epsilon }}_{\mathrm{o}}}$

• $\frac{{\mathrm{\varphi }}_2 + {\mathrm{\varphi }}_1}{{\mathrm{\epsilon }}_{\mathrm{o}}}$

• $\frac{{\mathrm{\varphi }}_1 - {\mathrm{\varphi }}_2}{{\mathrm{\epsilon }}_0}$

• ${\mathrm{\epsilon }}_0 \left({\mathrm{\varphi }}_1 + {\mathrm{\varphi }}_2 \right)$

Two long straight wires, each carrying an electric current of 5 A, are kept parallel to each other at a separation of 2.5 cm. Find the magnitude of the magnetic force experiment by 10 cm of a wire.

• 4.0 × 10^-4 N

• 3.5 × 10^-6 N

• 2.0 × 10^-5 N

• 2.0 × 10^-9 N

The parts of two concentric circular arcs joined by two radial lines and carries current i. The arcs subtend an angle 0 at the centre of the circle. The magnetic field at the centre O, is

• $\frac{{\mathrm{\mu }}_{0 }\mathrm{i}\left( \mathrm{b} - \mathrm{a} \right) \mathrm{\theta }}{4\mathrm{\pi } \mathrm{ab}}$

• $\frac{{\mathrm{\mu }}_0\mathrm{i} \left(\mathrm{b} - \mathrm{a}\right)}{\left(\mathrm{\pi } - \mathrm{\theta } \right)}$

• $\frac{{\mathrm{\mu }}_0\mathrm{i} \left( \mathrm{b} - \mathrm{a} \right)\mathrm{\theta }}{\mathrm{\pi ab}}$

• $\frac{{\mathrm{\mu }}_0\mathrm{i} \left(\mathrm{a} - \mathrm{b}\right)}{2\mathrm{\pi ab}}$

A square loop is made by a uniform conductor wire as shown in figure

The net magnetic field at the centre of the loop if side length of the square is a

• $\frac{{\mathrm{\mu }}_0 \mathrm{i}}{2 \mathrm{a}}$

• zero

• $\frac{{\mathrm{\mu }}_0 {\mathrm{i}}^2}{{\mathrm{a}}^2}$

• None of these

A thin bar magnet of length 2 L is bent at the mid-point so that the angle between them is 60°. The new length of the magnet is

• L/2√3

• √3 L/2

• L

• 2 L/3