## A solenoid of 2 m long & 3 cm diameter has 5 layer of windings of 500 turns per metre length in each layer & carries a current of 5 A…

Q: A solenoid of 2 m long & 3 cm diameter has 5 layer of windings of 500 turns per metre length in each layer & carries a current of 5 A. Find intensity of magnetic field at the centre of the solenoid.

Sol: For long solenoid at the centre , B = μ0 n i

$\large H = \frac{B}{\mu_0} = n i$

= (500 × 2)5 × 5

= 2.5 × 104 A/m.

## A toroid of non ferromagnetic has core of inner radius 25 cm and outer radius 26 cm. It has 3500 turns & carries a current of 11 A…

Q: A toroid of non ferromagnetic has core of inner radius 25 cm and outer radius 26 cm. It has 3500 turns & carries a current of 11 A , then find the magnetic field at a point

(i) In the internal cavity of toroid

(ii) At the midpoint of the windings

(iii) At a point which is at a distance of 30cm from the centre of toroid

Sol: (i) B = 0

(ii) $\large B = \mu_0 n i = \mu_0 (\frac{N}{2 \pi r}) i$

$\large B = \frac{\mu_0}{2 \pi} \frac{N i}{r}$

$\large B = 2 \times 10^{-7} \times \frac{3500 \times 11}{51 \times 10^{-2}/2}$

= 29.3 × 10-3 T

(iii) B = 0

## A solenoid 60 cm long and of radius 4.0 cm has 3 layers of windings of 300 turns each. A 2.0 cm long wire of mass 2.5 g lies inside the solenoid…

Q: A solenoid 60 cm long and of radius 4.0 cm has 3 layers of windings of 300 turns each. A 2.0 cm long wire of mass 2.5 g lies inside the solenoid (near its centre) normal to its axis, both the wire and the axis of the solenoid are in the horizontal plane. The wire is connected through two leads parallel to the axis of the solenoid to an external battery which supplies a current of 6.0 A in the wire. What value of current (with appropriate sense of circulation) in the windings of the solenoid can support the weight of the wire? g = 9.8 ms^(-2).

Sol: $\large m g = i_{wire} l B$

But , $\large B = \mu_0 n i_{solenoid}$

$\large m g = i_{wire} l \times \mu_0 n i_{solenoid}$

$\large i_{solenoid} = \frac{m g}{\mu_0 n i_{wire}\times l}$

= 108 A

## A solenoid of length 8 cm has 100 turns in it. If radius of coil is 3 cm and if it is carrying a current of 2 A…

Q: A solenoid of length 8 cm has 100 turns in it. If radius of coil is 3 cm and if it is carrying a current of 2 A, find the magnetic induction at a point 4 cm from the end on the axis of the solenoid.

Sol: $\large B = \frac{\mu_0 n i}{2} (sin\alpha + sin\beta)$

$\large B = \frac{4\pi \times 10^{-7}\times 100 \times 2}{2} (\frac{4}{5} + \frac{4}{5})$

= 64 π μT

## A magnetic needle is arranged at the centre of a current carrying coil having 50 turns with radius of coil ….

Q: A magnetic needle is arranged at the centre of a current carrying coil having 50 turns with radius of coil 20 cm arranged along magnetic meridian. When a current of 0.5 mA is allowed to pass through the coil the deflection is observed to be 30°. Find the horizontal component of earth’s magnetic field.

Sol: $\large B = B_H tan\theta$

$\large \frac{\mu_0 n i}{2 r} = B_H tan\theta$

$\large B_H = \frac{\mu_0 n i}{2 r tan \theta}$

$\large B_H = \frac{4 \pi \times 10^{-7} \times 50 \times 5 \times 10^{-4}}{2 \times 0.2 \times tan30^o}$

$\large = 5 \sqrt{3} \pi \times 10^{-8} T$

= 26.35  × 10-8 T

= 2.365  × 10-7 T