Question

The magnetic induction at a point $1$ $\stackrel{o}{A}$ away from a proton measured along its axis of spin is (magnetic moment of the proton is $1.4\times {10}^{-26}$A $m^2$).

• A. $0.28$ mT
• B. $28$ mT
• C. $0.028$ mT
• D. $2.8$ mT

Answer 1

Answer: (D)

$2.8$ mT

On the axis of a magnetic dipoles, magnetic induction is
$B=\frac{{\mu }_o}{4\pi }\times \frac{2m}{r^3}$

Here, $r=1$ $\stackrel{o}{A}={10}^{-10}$m, $m=1.4\times {10}^{-26}$A $m^{-2}$ and $\frac{\mu }{4\pi }={10}^{-7}$N $A^{-2}$

$\therefore B=\frac{{10}^{-7}\times 2\times 1.4\times {10}^{-26}}{({10}^{-10}{)}^3}=\frac{{10}^{-7}\times 2.8\times {10}^{-26}}{{10}^{-30}}$
$=2.8\times {10}^{-3}$T $=2.8$mT.