A tightly- wound solenoid of radius a and length l has n turns per unit length. It carries an
Channel: Doubtnut
Date: 2020-07-05

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.