If the radius of the dees of cyclotron is r, then the kinetic energy of a proton of mass m accelerated by the cyclotron at an oscillating frequency v is

• $4{\mathrm{\pi }}^2{\mathrm{m}}^2{\mathrm{v}}^2{\mathrm{r}}^2$

• $4{\mathrm{\pi }}^2{\mathrm{mv}}^2{\mathrm{r}}^2$

• $2{\mathrm{\pi }}^2{\mathrm{mv}}^2{\mathrm{r}}^2$

• ${\mathrm{\pi }}^2{\mathrm{mv}}^2{\mathrm{r}}^2$

If a magnetic dipole of moment M situated in the direction of a magnetic field B is rotated by 180°, then the amount of work done is

• MB

• 2 MB

• $\frac{\mathrm{MB}}{\sqrt{2}}$

• Zero

The magnetic field at a point midway between two parallel long wires carrying currents in the same direction is 10 µT. If the direction of the smaller current among them is reversed, the field becomes 30 µT. The ratio of the larger to the smaller current in them is

• 3 : 1

• 2 : 1

• 4 : 1

• 3 : 2

A 100 turns coil of area of cross-section 200 cm² having 2 Ω resistance is held perpendicular to a magnetic field of 0.1 T. If it is removed from the magnetic field in one second, the induced charge produced in it is

• 0.2 C

• 2 C

• 0.1 C

• 1 C

A galvanometer connected with an unknown resistor and two identical cells in series each of emf 2 V shows a current of 1 A. If the cells are connected in parallel, it shows 0.8 A. Then, the internal resistance of the cell is

• 1 Ω

• 0.5 Ω

• 0.25 Ω

• 0.33 Ω

The shunt resistance required to allow 4% of the main current through the galvanometer of resistance 48 Ω is

• 1 Ω

• 2 Ω

• 3 Ω

• 4 Ω

A straight wire carrying current I is made into a circular loop. If M is the magnetic moment associated with the loop, then the length of the wire is

• $\sqrt{\frac{4\mathrm{\pi M}}{\mathrm{I}}}$

• $\sqrt{\frac{2\mathrm{\pi M}}{\mathrm{I}}}$

• $\sqrt{\frac{\mathrm{\pi M}}{\mathrm{I}}}$

• $\sqrt{\frac{\mathrm{\pi M}}{2\mathrm{I}}}$

An electron moving around the nucleus with an angular momentum l has a magnetic moment

• $\frac{\mathrm{e}}{\mathrm{m}} \mathrm{l}$

• $\frac{\mathrm{e}}{2\mathrm{m}} \mathrm{l}$

• $\frac{2\mathrm{e}}{\mathrm{m}} \mathrm{l}$

• $\frac{\mathrm{e}}{2\mathrm{\pi m}} \mathrm{l}$

A magnetic needle lying parallel to a magnetic field requires W units of work to turn it through 60°. The torque required to keep the needle in this position will be

• 2W

• W

• $\sqrt{3} \mathrm{W}$

• $\frac{\mathrm{W}}{\sqrt{3}}$

Two identical magnetic dipoles of magnetic moment 2 Am² are placed at a separation of 2 m with their axis perpendicular to each other in air. The resultant magnetic field at a midpoint between the dipoles is

• $4\sqrt{5} \times {10}^{-5} \mathrm{T}$

• $2\sqrt{5} \times {10}^{-5} \mathrm{T}$

• $4\sqrt{5} \times {10}^{-7} \mathrm{T}$

• $2\sqrt{5} \times {10}^{-7} \mathrm{T}$