Question

A bar magnet has pole strength $1Am$ and is placed as shown in Fig. $24.19$(a). Find the magnetic field at $P$.

• A. $11\mu T$
• B. $14\mu T$
• C. $19\mu T$
• D. $22\mu T$

Answer 1

The correct option is D $22\mu T$

$SN=6cm$, $SP=8cm$, $NP=\sqrt{8^2+6^2}=10cm$
Magnetic field due to south pole is $B_S=\frac{{\mu }_{0}M}{4\pi r^2}=\frac{{\mu }_{0}M}{4\pi (8\times {10}^{-2}{)}^2}$
Magnetic field due to north pole is $B_N=\frac{{\mu }_{0}M}{4\pi r^2}=\frac{{\mu }_{0}M}{4\pi (10\times {10}^{-2}{)}^2}$
$B=\sqrt{B_S^2+B_N^2+2B_S{B}_N\cos 143}$
$B=\sqrt{B_S^2+B_N^2+2B_S{B}_N\cos (90+53)}$
$B=\frac{{\mu }_{0}M}{4\pi }\sqrt{\frac{1}{(8\times {10}^{-2}{)}^2}+\frac{1}{(10\times {10}^{-2}{)}^2}-\frac{2\times 1}{(8\times {10}^{-2}{)}^2}\times \frac{1}{(10\times {10}^{-2}{)}^2}\sin 53}$
$B=0.22\times {10}^{-4}T=22\mu T$