A tightly wound solenoid of radius 'a' and length 'l' has n turns per unit length. It carries an electric current i. Magnetic field at a distance `(l)/(4)` from one of the end (inside the solenoid on its axis) is `B=(mu_(0)ni(sqrt5+3))/(sqrtK)` for `l=4a`. Then find the value of K.

A tightly- wound solenoid of radius a and length l has n turns per unit length. It carries an electric current i. Consider a length dx of the solenoid at a distance x from one end. This contains n dx turns and may be approximated as a circular current I n dx. (a) Write the magnetic field at the centre of the solenoid due to this circular current. Integrate this expression under proper limits to find the magnetic field at the centre of the solenoid. (b) Verify that if lgtgta , the field tends to (B=(mu_0)ni) and if agtgt1 , the field tends to B= ((mu_0)nil/2a) . Interpret these results.

A tightly- wound solenoid of radius a and length l has n turns per unit length. It carries an electric current i. Consider a length dx of the solenoid at a distance x from one end. This contains n dx turns and may be approximated as a circular current I n dx. (a) Write the magnetic field at the center of the solenoid due to this circular current. Integrate this expression under proper limits to find the magnetic field at the center of the solenoid. (b) Verify that if lgtgta , the field tends to (B=(mu_0ni) and if agtgt1 , the field tends to B= ((mu_0)nil/2a) . Interpret these results.

A tightly- wound solenoid of radius a and length l has n turns per unit length. It carries an electric current i. Consider a length dx of the solenoid at a distance x from one end. This contains n dx turns and may be approximated as a circular current I n dx. (a) Write the magnetic field at the center of the solenoid due to this circular current. Integrate this expression under proper limits to find the magnetic field at the center of the solenoid. (b) Verify that if lgtgta , the field tends to (B=(mu_0ni) and if agtgt1 , the field tends to B= ((mu_0)nil/2a) . Interpret these results.

A long solenoid has a radius a and number of turns per unit length is n . If it carries a current i, then the magnetic field on its axis is directly proportional to

A long solenoid has a radius a and number of turns per unit length is n . If it carries a current i, then the magnetic field on its axis is directly proportional to

The magnetic field on the axis of a long solenoid having n turns per unit length and carrying a current is

A solenoid of radius R and length L has a current I = I​_0 cosωt. The value of induced electric field at a distance of r outside the solenoid, is