In a chamber, a uniform magnetic field of $6.5 ~\text G~ (1 ~\text G = 10^{–4}~\text  T)$ is maintained. An electron is shot into the field with a speed of $4.8 × 10 ^6~\text{ms}^{–1}$ normal to the field. the radius of the circular orbit is:
$(\text{take}~e = 1.6 × 10^{–19}~\text  C,  ~𝑚_𝑒  = 9.1×10^{–31}~\text{kg})$
1. $4.2~\text{cm}$
2. $5.3~\text{cm}$
3. $4.7~\text{cm}$
4. $5.2~\text{cm}$

A circular coil of $30$ turns and a radius of $8.0$ cm carrying a current of $6.0$ A is suspended vertically in a uniform horizontal magnetic field of magnitude $1.0$ T. The field lines make an angle of $60^\circ$ with the normal of the coil. What will be the magnitude of the counter-torque that must be applied to prevent the coil from turning?
1. $7.12$ N-m
2. $3.13$ N-m
3. $6.50$ N-m
4. $4.44$ N-m

Two concentric circular coils X and Y of radii 16 cm and 10 cm, respectively, lie in the same vertical plane containing the north to south direction. Coil X has 20 turns and carries a current of 16 A, coil Y has 25 turns and carries a current of 18 A. The sense of the current in X is anticlockwise, and clockwise in Y, for an observer looking at the coils facing west. The magnitude and direction of the net magnetic field due to the coils at their centre is:
1. $2 \pi \times 10^{-4}\text{ T (East)}$
2. $5 \pi \times 10^{-4}\text{ T (East)}$
3. $5 \pi \times 10^{-4}\text{ T (West)}$
4. $4 \pi \times 10^{-4}\text{ T(West)}$

For a circular coil of radius R and N turns carrying current I, the magnitude of the magnetic field at a point on its axis at a distance x from its centre is given by, $B=\frac{\mu_0 I R^2 N}{2\left(x^2+R^2\right)^{\frac{3}{2}}}$

The magnetic field at the centre of the coil is:
1. $\frac{\mu_0 I N}{R}$
2. $\frac{2 \mu_0 I N}{R}$
3. $0$
4. $\frac{\mu_0 I N}{2 R}$

A toroid has a core (non-ferromagnetic) of inner radius 25 cm and outer radius 26 cm, around which 3500 turns of a wire are wound. If the current in the wire is 11 A, the magnetic field inside the core of the toroid is:

1. 3×10^-2 T
2. 0
3. 2×10^-3 T
4. 1×10^-2 T

An electron emitted by a heated cathode and accelerated through a potential difference of 2.0 kV, enters a region with a uniform magnetic field of 0.15 T. if the field is transverse to its initial velocity, the radius of the circular path is:

1. 2.10 mm
2. 0.11 mm
3. 1.01 mm
4. 0.12 mm

A circular coil of wire consisting of 100 turns, each of radius 8.0 cm carries a current of 0.40 A. What is the magnitude of the magnetic field B at the centre of the coil?

1.$3.14 \times 10^{-4} \ T$ 
2.$2.12 \times 10^{-4} \ T$ 
3.$1.41 \times 10^{-4} \ T$ 
4.$2.01 \times 10^{-4} \ T$
 

A long straight wire carries a current of $35~\text{A}.$ The magnitude of the magnetic field at a point $20~\text{cm}$ from the wire is:
1. $3.5 \times 10^{-6} ~\text T$
2. $3.5 \times 10^{-5} ~\text T$
3. $4.5 \times 10^{-6} ~\text T$
4. $4.5 \times 10^{-5} ~\text T$

A long straight wire in the horizontal plane carries a current of 50 A in the north to south direction. The magnitude and direction of the magnetic field at a point 2.5 m east of the wire is:
1. $4 \times 10^{-6}~ T$ vertically upward
2. $4 \times 10^{-6} ~T$ vertically downward
3. $3 \times 10^{-6} ~T$ vertically upward
4. $3 \times 10^{-6} ~T$ vertically downward

A horizontal overhead power line carries a current of $90$ A in the east to west direction. What is the magnitude and direction of the magnetic field due to the current $1.5~\text{m}$ below the line?