The oscillating frequency of a cyclotron is 10 MHz. If the radius of its dees is 0.5 m, the kinetic energy of a proton, which is accelerated by the cyclotron is

• 10.2 MeV

• 2.55 MeV

• 20.4 MeV

• 5.1 MeV

72.

A plane electromagnetic wave travelling along the X- direction has a wavelength of 3 mm. The variation in the electric field occurs in the Y-direction with an amplitude 66 Vm^-1. The equations for the electric and magnetic fields as a function of x and t are respectively.

• $$\begin{gathered} {\mathrm{E}}_{\mathrm{y}} = 33 \cos \mathrm{\pi } \times {10}^{11} \left(\mathrm{t} - \frac{\mathrm{x}}{\mathrm{c}}\right) \\ {\mathrm{B}}_{\mathrm{z}} = 1.1 \times {10}^{-7} \cos \mathrm{\pi } \times {10}^{11} \left(\mathrm{t} - \frac{\mathrm{x}}{\mathrm{c}}\right) \end{gathered}$$

• $$\begin{gathered} {\mathrm{E}}_{\mathrm{y}} = 11 \cos 2\mathrm{\pi } \times {10}^{11} \left(\mathrm{t} - \frac{\mathrm{x}}{\mathrm{c}}\right) \\ {\mathrm{B}}_{\mathrm{y}} = 11 \times {10}^{-7} \cos 2\mathrm{\pi } \times {10}^{11} \left(\mathrm{t} - \frac{\mathrm{x}}{\mathrm{c}}\right) \end{gathered}$$

• $$\begin{gathered} {\mathrm{E}}_{\mathrm{x}} = 33 \cos \mathrm{\pi } \times {10}^{11} \left(\mathrm{t} - \frac{\mathrm{x}}{\mathrm{c}}\right) \\ {\mathrm{B}}_{\mathrm{x}} = 11 \times {10}^{-7} \cos \mathrm{\pi } \times {10}^{11} \left(\mathrm{t} - \frac{\mathrm{x}}{\mathrm{c}}\right) \end{gathered}$$

• $$\begin{gathered} {\mathrm{E}}_{\mathrm{y}} = 66 \cos 2\mathrm{\pi } \times {10}^{11} \left(\mathrm{t} - \frac{\mathrm{x}}{\mathrm{c}}\right) \\ {\mathrm{B}}_{\mathrm{z}} = 2.2 \times {10}^{-7} \cos 2\mathrm{\pi } \times {10}^{11} \left(\mathrm{t} - \frac{\mathrm{x}}{\mathrm{c}}\right) \end{gathered}$$

A uniform electric field and a uniform magnetic field exist in a region in the same direction. An electron is projected with a velocity pointed in the same direction. Then the electron will 

• be deflected to the left without increase in speed

• be deflected to the right without increase in speed

• not be deflected but its speed will decrease

• not be deflected but its speed will increase

A galvanometer of resistance 20 Ω shows a deflection of 10 division when a current of 1 mA is passed through it. If a shunt of 4 Ω is connected and there are 50 division on the scale, the range of the galvanometer is

• 1 A

• 3 A

• 30 mA

• 30 A

A conducting rod of 1 m length and 1 kg mass is suspended by two vertical wires through its ends. An external magnetic field of 2 T is applied normal to the rod. Now the current to be passed through the rod so as to make the tension in the wires zero is [Take g = 10 ms^-2]

• 0.5 A

• 15 A

• 5 A

• 1.5 A

A circular coil of 5 turns and of 10 cm mean diameter is connected to a voltage source. If the resistance of the coil is 10 Ω, the voltage of the source so as to nullify the horizontal component of earth's magnetic field of 30 A turn m^-1 at the centre of the coil should be

• 6 V, plane of the coil normal to magnetic meridian

• 2 V, plane of the coil normal to magnetic meridian

• 6 V, plane of the coil along the magnetic meridian

• 2 V, plane of the coil along the magnetic meridian

A square coil of side 25 cm having 1000 turns is rotated with a uniform speed in a magnetic field about an axis perpendicular to the direction of the field. At an instant t, the emf induced in the coil is e = 200 sin 100 πt. The magnetic induction is

• 0.50 T

• 0.02 T

• 0.01 T

• 0.1 T

A magnetised wire of magnetic moment M and length L is bent in the form of a semi circle of radius r. The new magnetic moment is 

• M

• $\frac{\mathrm{M}}{2\mathrm{\pi }}$

• $\frac{\mathrm{M}}{\mathrm{\pi }}$

• $\frac{2\mathrm{M}}{\mathrm{\pi }}$

A proton, a deuteron and an alpha particle with the same kinetic energy enter a region of uniform magnetic field B at right angles to the field. The ratio of the radii of their circular paths is

• 1 : 1 : 1

• $1 : \sqrt{2} : \sqrt{2}$

• $\sqrt{2} : 1 : 1$

• $\sqrt{2} : \sqrt{2} : 1$

A solenoid 600 mm long has 50 turns on it and is wound on an iron rod of 7.5 mm radius. Find the flux through the solenoid when the current in it is 3 A. The relative permeability of iron is 600

• 1.66 Wb

• 1.66 n Wb

• 1.66 m Wb

• 1.66 μ Wb