Question

A circular coil of radius \(10\,\text{cm}\) is carrying a current. From the centre of the coil, the distance of a point on its axis where \[ \frac{dB}{dx} \] becomes maximum is \[ \left( \frac{dB}{dx} \text{ is the rate of change of magnetic field with distance }x \text{ from the centre of the coil} \right) \]

• A. \(40\,\text{cm}\)
• B. \(20\,\text{cm}\)
• C. \(10\,\text{cm}\)
• D. \(5\,\text{cm}\)

Hint:

For a circular current-carrying coil, \[ \boxed{ B=\frac{\mu_0IR^2}{2(R^2+x^2)^{3/2}}. } \] The magnitude of the field gradient is maximum at \[ \boxed{x=\frac{R}{2}.} \]

Answer 1

The Correct Option is D