A cylindrical coil of radius r, having n turns per unit length and carrying a current I has a magnetic field near its one end equal to:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( \displaystyle\frac{\mu_0nI}{2} \)
A long cylindrical coil is a solenoid. Deep inside it the field is uniform with magnitude \( B = \mu_0nI \). Near an end, only half of the turns lie on one side of the point, and by symmetry the field there is half the value at the centre.
\( \displaystyle B_{\mathrm{end}} = \frac{1}{2}\mu_0nI = \frac{\mu_0nI}{2} \)
The radius r does not appear in the field of a long solenoid, so Options (2) and (3) cannot be right; they also do not have the dimension of a magnetic field.