Question

A current carrying circular loop of radius 'R' and current carrying long straight wire are placed in the same plane. I, and I are the currents through circular loop and long straight wire respectively. The perpendicular distance between centre of the circular loop and wire is *d'. The magnetic field at the centre of the loop will be zero when separation 'd' is equal to

• A. R/π

Answer 1

Answer: (A)

R/π

Answer 2

Solution Explanation:

1. Magnetic Field due to the Loop:
   At the center of a circular loop of radius $R$ carrying current $I$, the magnetic field is given by

   $$B_{\text{loop}} = \frac{\mu_0 I}{2R}.$$

2. Magnetic Field due to the Long Straight Wire:
   The magnetic field at a distance $d$ from a long straight wire carrying current $I$ is

   $$B_{\text{wire}} = \frac{\mu_0 I}{2\pi d}.$$

3. Condition for Zero Net Magnetic Field:
   For the net field at the center of the loop to be zero, the magnitudes of the two fields must be equal (and opposite in direction):

   $$\frac{\mu_0 I}{2R} = \frac{\mu_0 I}{2\pi d}.$$

   Canceling the common factors gives:

   $$\frac{1}{2R} = \frac{1}{2\pi d} \quad \Rightarrow \quad \pi d = R \quad \Rightarrow \quad d = \frac{R}{\pi}.$$

Answer:
The separation $d$ must be equal to $\frac{R}{\pi}$.