Two circular loops of radii 5 cm and 10 cm lie in the same plane and have the same centre. The inner loop carries a current of 2 A. The current in the outer loop flows in the opposite sense. The net magnetic field at the common centre is zero when the current in the outer loop is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 4 A
The field at the centre of a circular loop is \(B_0=\mu_0I/2R\). By the right-hand thumb rule, currents in opposite senses give fields in opposite directions at the centre. So the net field is zero when the two fields are equal in size.
Inner loop: \(I_1=2\ \mathrm{A}\), \(R_1=5\ \mathrm{cm}\)
Outer loop: \(R_2=10\ \mathrm{cm}\)
\( \begin{aligned} \frac{\mu_0 I_2}{2R_2} &= \frac{\mu_0 I_1}{2R_1} \\ I_2 &= I_1\times\frac{R_2}{R_1} \\ &= 2\times\frac{10}{5} \\ &= 4\ \mathrm{A} \end{aligned} \)
A larger loop gives a weaker field for the same current. So the outer loop needs twice the current of the inner loop.
NCERT (2026-27):
Magnetic Field on the Axis of a Circular Current Loop – “As a special case of the above result, we may obtain the field at the centre of the loop. Here x = 0, and we obtain,”
\( B_0=\frac{\mu_0 I}{2R}\,\hat{i} \)\( \qquad (4.12) \)
Magnetic Field on the Axis of a Circular Current Loop – “Curl the palm of your right hand around the circular wire with the fingers pointing in the direction of the current. The right-hand thumb gives the direction of the magnetic field.”