The magnetic field strength due to a short bar magnet directed along its axial line at a distance r is B. What is its value at the same distance along the equatorial line?

CONCEPT:

Magnetic field

• A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials.
• A charge that is moving in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field.
• Moving charges will generate a magnetic field.​​

Magnetic dipole

• A Magnetic Dipole consists of two unlike poles of equivalent strength and separated by a small distance.
• Magnetic moment: It is defined as the product of pole strength and the distance between the poles of a magnet.

​⇒ M = m × l

where M = magnetic moment, m = pole strength and l = distance between the poles

CALCULATION:

• The magnetic field at any axial point is given as,

\(\Rightarrow B_{a}=\frac{2\mu_{o}}{4\pi r^{3}}\)     -----(1)

• The magnetic field at any equatorial point is given as,

\(\Rightarrow B_{e}=\frac{\mu_{o}}{4\pi r^{3}}\)

\(\Rightarrow B_{e}=\frac{1}{2}\frac{2\mu_{o}}{4\pi r^{3}}\)

\(\Rightarrow B_{e}=\frac{B_{a}}{2}\)           [∵ B_a = B]

\(\Rightarrow B_{e}=\frac{B}{2}\)

• Hence, option 3 is correct.