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5.Magnetism and Matter
hard
Two identical dipoles each of magnetic moment $1.0\, A-m^2$ are placed at a separation of $2\,m$ with their axes perpendicular to each other. What is the magnetic field at a point midway between the dipoles ?
A
$\sqrt 5 \times \, 10^{-7} \,T$
B
$3 \times \, 10^{-7} \,T$
C
$\sqrt 3 \times \, 10^{-7} \,T$
D
$5 \times \, 10^{-7} \,T$
Solution
$\mathrm{B}_{\mathrm{ret}}=\sqrt{\mathrm{B}_{1}^{2}+\mathrm{B}_{2}^{2}}$
$\mathrm{B}_{\text {ret }}=\sqrt{\left(2 \frac{\mu_{0}}{4 \pi} \frac{\mathrm{M}}{\mathrm{r}^{3}}\right)^{2}+\left(\frac{\mu_{0} \mathrm{M}}{4 \pi \mathrm{r}^{3}}\right)^{2}}$
$\mathrm{B}_{\mathrm{ret}}=\sqrt{5} \frac{\mu_{0}}{4 \pi \mathrm{r}^{3}}=\sqrt{5} \times 10^{-7} \times \frac{1}{(1)^{3}}=\sqrt{5} \times 10^{-7} \,\mathrm{T}$
Standard 12
Physics
