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

58.

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

• $\frac{\mathrm{R}}{\sqrt{3}}$

• $\sqrt{3} \mathrm{R}$

• 2 $\sqrt{3}$ R

• $\frac{2 \mathrm{R}}{\sqrt{3}}$

A current carrying loop is placed in a uniform magnetic field in four different orientations I, II, III and IV as shown in figure. Arrange them in decreasing order of potential energy

• l > lll> ll > lV

• l > ll > lll > lV

• l > lV > ll > lll

• lll > lV > l > ll

A current I is flowing through the loop. The direction of the current and the shape of the loop are as shown in the figure. The magnetic field at the centre of the loop is μ₀I/R times ( MA = R, MB = 2R, ∠DMA = 90^o )

• 5/16, but out of the plane of the paper.

• 5/16, but into the plane of the paper.

• 7/16, but out of the plane of the paper.

• 7/16, but into the plane of the paper.