Moving perpendicular to field B, a proton and an alpha particle both enter an area of uniform magnetic field B. If the kinetic energy of the proton is 1 MeV and the radius of the circular orbits for both particles is equal, the energy of the alpha particle will be:

1. 4 MeV

2. 0.5 MeV

3. 1.5 MeV

4. 1 MeV

A rectangular coil of length 0.12 m and width 0.1 m having 50 turns of wire is suspended vertically in a uniform magnetic field of strength 0.2 Wb/m². The coil carries a current of 2 A. If the plane of the coil is inclined at an angle of 30^o with the direction of the field, the torque required to keep the coil in stable equilibrium will be:

1. 0.15 N-m

2. 0.20 N-m

3. 0.24 N-m

4. 0.12 N-m

A wire carrying current I has the shape as shown in the adjoining figure. Linear parts of the wire are very long and parallel to X-axis while the semicircular portion of radius R is lying in the Y –Z plane. The magnetic field at point O is:

   
 

1. \(B=\frac{\mu i }{4\pi R}\left ( \pi \hat{i}+2\hat{k} \right )\)
2. \(B=-\frac{\mu i }{4\pi R}\left ( \pi \hat{i}-2\hat{k} \right )\)
3. \(B=-\frac{\mu i }{4\pi R}\left ( \pi \hat{i}+2\hat{k} \right )\)

4. \(B=\frac{\mu i }{4\pi R}\left ( \pi \hat{i}-2\hat{k} \right )\)

An electron moving in a circular orbit of radius r makes n rotations per second. The magnetic field produced at the centre has a magnitude:

1. μ₀ne/2πr

2. zero

3. n²e/r

4. μ₀ne/2r

In an ammeter, \(0.2 \%\) of the main current passes through the galvanometer. If the resistance of the galvanometer is \(G,\) the resistance of the ammeter will be:

Two identical long conducting wires AOB and COD are placed at a right angle to each other, with one above the other such that 'O' is the common point for the two. The wires carry I₁ and I₂ currents, respectively. Point 'P' is lying at a distance 'd' from 'O' along a direction perpendicular to the plane containing the wires. What will be the magnetic field at the point "P"?

1. $\frac{{\mu }_0}{2\mathrm{\pi d}}\left(\frac{I_1}{I_2}\right)$

2. $\frac{{\mu }_0}{2\mathrm{\pi d}}\left(I_1+I_2\right)$

3. $\frac{{\mu }_0}{2\mathrm{\pi d}}\left(I_1^2+I_2^2\right)$

4. $\frac{{\mu }_0}{2\mathrm{\pi d}}{\left(I_1^2+I_2^2\right)}^{1/2}$

When a proton is released from rest in a room, it starts with an initial acceleration a₀ towards the east. When it is projected towards the north with a speed of v₀, it moves with an initial acceleration of 3a₀ towards the east. What are the electric and magnetic fields in the room?