A long solenoid of 50 cm length having 100 turns carries a current of 2.5 A. The magnetic field at the centre of the solenoid is:

$\left({\mathrm{\mu }}_0=4\mathrm{\pi }\times {10}^{-7} \mathrm{T} \mathrm{m} {\mathrm{A}}^{-1}\right)$

1.  $3.4\times {10}^{-4}T$

2.  $6.28\times {10}^{-5}T$

3.  $3.14\times {10}^{-5}T$

4.  $6.28\times {10}^{-4}T$

In a chamber, a uniform magnetic field of 6.5 G (1 G = 10^–4 T) is maintained. An electron is shot into the field with a speed of 4.8 ×${10}^6$ m s^–1 normal to the field. the radius of the circular orbit is:
(e = 1.6 × 10^–19 C, $m_e$ = 9.1×10^–31 kg)

$$\begin{gathered} \left(1\right) 4.2 cm \\ \left(2\right) 5.3 cm \\ \left(3\right) 4.7 cm \\ \left(4\right) 5.2 cm \end{gathered}$$

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° 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:

$$\begin{gathered} \left(1\right) 2\pi \times {10}^{-4} T \left(East\right) \\ \left(2\right) 5\pi \times {10}^{-4} T \left(East\right) \\ \left(3\right) 5\pi \times {10}^{-4} T \left(West\right) \\ \left(4\right) 4\pi \times {10}^{-4} T \left(West\right) \end{gathered}$$

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, $B=\frac{{\mu }_{0}I{R}^{2}N}{2{\left(x^2+R^2\right)}^{{\displaystyle \frac{3}{2}}}}$

The magnetic field at the centre of the coil is:

$$\begin{gathered} \left(1\right) \frac{{\mu }_{0}I N}{R} \\ \left(2\right) \frac{2{\mu }_{0}I N}{R} \\ \left(3\right) 0 \\ \left(4\right) \frac{{\mu }_{0}I N}{2R} \end{gathered}$$

A closely wound solenoid of 2000 turns and area of cross-section as \(1.6\times10^{-4}\) m², carrying a current of 4.0 A, is suspended through its center allowing it to turn in a horizontal plane. The magnetic moment associated with the solenoid is:

1. 0.18 Am²
2. 3.24 Am²
3. 1.28 Am²
4. 0.38 Am²

A monoenergetic electron beam with an electron speed of 5.20 x 10⁶ m/s is subject to a magnetic field of 1.30 x 10^-4 T normal to the beam velocity. What is the radius of the circle traced by the beam, given e/m for electron equals 1.76 x 10¹¹ C kg^-1?

(1) 22.7 cm

(2) 21.3 cm

(3) 20.0 cm

(4) 21.9 cm

An electron gun with its collector at a potential of 100 V fires out electrons in a spherical bulb containing hydrogen gas at low pressure $\left(~{10}^{-2} mm of Hg\right).$ A magnetic field of $2.83\times {10}^{-4} T$ curves the path of the electrons in a circular orbit of radius 12.0 cm. (The path can be viewed because the gas ions in the path focus the beam by attracting electrons, and emitting light by electron capture; this method is known as the 'fine beam tube' method. Specific charge ratio (e/m) is:

$$\begin{gathered} \left(1\right) 1.21\times {10}^{11} C k{g}^{-1} \\ \left(2\right) 1.73\times {10}^{11} C k{g}^{-1} \\ \left(3\right) 2.53\times {10}^{11} C k{g}^{-1} \\ \left(4\right) 3.02\times {10}^{11} C k{g}^{-1} \end{gathered}$$

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:

$$\begin{gathered} \left(1\right) 3\times {10}^{-2} T \\ \left(2\right) 0 \\ \left(3\right) 2\times {10}^{-3} T \\ \left(4\right) 1\times {10}^{-2} T \end{gathered}$$

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