Question

Magnetic induction on the axial line due to a short bar magnet is _____________ .

• A. $\frac{{\mu }_{o}4M}{4\pi d^3}N(A-m{)}^{-1}$
• B. $\frac{{\mu }_{o}M}{4\pi d^3}N(A-m{)}^{-1}$
• C. $\frac{{\mu }_{o}2M}{4\pi d^3}N(A-m{)}^{-1}$
• D. $\frac{{\mu }_{o}8M}{4\pi d^3}N(A-m{)}^{-1}$

Answer 1

The correct option is C $\frac{{\mu }_{o}2M}{4\pi d^3}N(A-m{)}^{-1}$

We know that magnetic induction on the axial line due to a bar magnet is $\frac{{\mu }_{0}2Md}{4\pi (d^2-l^2{)}^2}$

where,

M = Magnetic moment

l = lenth of magnet

d = distance

But, for a short bar magnet where $l<<d$

So $(d^2-l^2)$ can be taken as $d^2$

Magnetic on the axial line due to a short bar magnet is $\frac{{\mu }_{0}2M}{4\pi d^3}N(A-m{)}^{-1}$

Therefore, C is correct option