Question

Magnetic induction at a point along the axis of a bar magnet is equal to magnetic induction at a point along the equator. The ratio of the distance along the axis to distance along equator is:

• A. \( \sqrt{2} : 1 \)
• B. 2 : 1
• C. \( 3\sqrt{2} : 1 \)
• D. \( 1 : \sqrt{2} \)

Hint:

In a bar magnet, the magnetic field strength along the axis and equator are related, and their ratio can be derived using the formulas for magnetic induction at these points.

Answer 1

The Correct Option is C

Step 1: Formula for Magnetic Induction.
The magnetic induction along the axis of a bar magnet is given by: \[ B_{\text{axis}} = \frac{\mu_0}{4 \pi} \cdot \frac{2M}{r^3} \] and the magnetic induction along the equator is: \[ B_{\text{equator}} = \frac{\mu_0}{4 \pi} \cdot \frac{M}{r^3} \] where \( M \) is the magnetic moment, \( r \) is the distance from the magnet, and \( \mu_0 \) is the permeability of free space. Since the magnetic induction at both points is equal, the ratio of distances is: \[ \frac{r_{\text{axis}}}{r_{\text{equator}}} = 3\sqrt{2} \] Step 2: Final Answer.
Thus, the ratio of the distance along the axis to the distance along the equator is \( 3\sqrt{2} : 1 \).