Question

The current through a circular coil is halved and the radius of the coil is doubled. If $B_1$ and $B_2$ are respectively the initial and final magnetic field strengths at the center of the coil, then:

• A. $B_2 = \frac{B_1}{2}$
• B. $B_2 = 4B_1$
• C. $B_2 = 2B_1$
• D. $B_2 = \frac{B_1}{4}$

Hint:

Since magnetic field strength is directly proportional to current and inversely proportional to radius, halving the current cuts the field in half ($\frac{1}{2}$), and doubling the radius cuts it in half again ($\frac{1}{2}$). Combining these updates gives $\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$ of the original strength!

Answer 1

The Correct Option is D