Question

Two concentric solenoids carry currents in opposite directions. The inner solenoid has 50 turns per cm. The outer

solenoid has 20 turns per cm. The inner coil carries a current of 0.5 A. (a) Calculate the current needed in the

outer coil so that its fields cancels the field produced by the inner coil. (b) How large a field is produced by the

inner coil?

Answer 1

Assuming the solenoids are equal and the only difference is the current and number of turns, for equal magnetic fields, we can write:

$$N_1I_1=N_2I_2,\\ I_2=I_1N_1/N_2=1.25.$$

The field is

$$B=\dfrac{N_1I_1}{L_1}=25/L\text{ T},$$

where L is the length of the solenoid.