Question

The magnetic induction at a point $1A^0$ 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. $0.28mT$
• B. $28mT$
• C. $0.028mT$
• D. $2.8mT$

Answer 1

Answer: (D)

$2.8mT$

On the axis of a magnetic dipoles, magnetic induction is
$B=\frac{{\mu }_0}{4\pi }\times \frac{2m}{r^3}$
Here, $r=1A={10}^{-10}m,m=1.4\times {10}^{-26}A{m}^{-2}and\frac{\mu }{4\pi }={10}^{-7}N{A}^{-2}$
$\therefore B=\frac{{10}^{-7}\times 2\times 1.4\times {10}^{-26}}{({10}^{-10}{)}^3}=\frac{{10}^{-7}\times 2.8\times {10}^{-26}}{{10}^{-30}}=2.8\times {10}^{-3}T=2.8mT$