A coil in the shape of an equilateral triangle of side l is suspended between the pole pieces of a permanent magnet such that B is in plane of the coil. If due to current i in the triangle a torque T acts on it, the side l of the triangle is

An electron moves in a circular orbit with a uniform speed v. It produces a magnetic field B at the centre of the circle. The radius of the circle is proportional, to

• B/v

• v/B

• √v/B

• √B/v

In a mass spectrometer used for measuring the masses of ions, the ions are initially accelerated by an electric potential V and then made to describe semicircular paths of radius R using a magnetic field B. If V and B are kept constant the ratio $\left(\frac{\mathrm{charge} \mathrm{on} \mathrm{the} \mathrm{ion}}{\mathrm{mass} \mathrm{of} \mathrm{the} \mathrm{ion}}\right)$ will be proportional to

• $\frac{1}{\mathrm{R}}$

• $\frac{1}{{\mathrm{R}}^2}$

• R²

• R

The north pole of a long horizontal bar magnet is being brought closer to a vertical conducting plane along the perpendicular direction. The direction of the induced current in the conducting plane will be

• horizontal

• vertical

• clockwise

• Anticlockwise

An electric current passes through a long straight copper wire. At a distance 5 cm from the straight wire, the magnetic field is B. The magnetic field at 20 cm from the straight wire would be

• $\frac{\mathrm{B}}{6}$

• $\frac{\mathrm{B}}{4}$

• $\frac{\mathrm{B}}{3}$

• $\frac{\mathrm{B}}{2}$

An electron of mass m and charge q is travelling with a speed v along a circular path of radius r at right angles to a uniform magnetic field B. If speed of the electron is doubled and the magnetic field is halved, then resulting path would have a radius of

• $\frac{\mathrm{r}}{4}$

• $\frac{\mathrm{r}}{2}$

• 2r

• 4r

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

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

50.

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

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

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

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

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