Question 29: Magnetism and Matter

Question

Figure shows a current carrying square loop ABCD of edge length is ‘a’ lying in a plane. If the resistance of the ABC part is r and that of ADC part is 2r, then the magnitude of the resultant magnetic field at centre of the square loop is

Accepted Answer

$\overrightarrow{\mathrm{B}}=\overrightarrow{\mathrm{B}}_{\mathrm{AB}}+\overrightarrow{\mathrm{B}}_{\mathrm{BC}}+\overrightarrow{\mathrm{B}}_{\mathrm{CD}}+\overrightarrow{\mathrm{B}}_{\mathrm{DA}}$
$$\begin{aligned}
\overrightarrow{\mathrm{B}}= & {\left[\frac{-\mu_0(2 \mathrm{I} / 3)}{4 \pi(\mathrm{a} / 2)} \sqrt{2}-\frac{\mu_0(2 \mathrm{I} / 3)}{4 \pi(\mathrm{a} / 2)} \sqrt{2}ight.} \
& \left.+\frac{\mu_0(\mathrm{I} / 3)}{4 \pi(\mathrm{a} / 2)} \sqrt{2}+\frac{\mu_0(\mathrm{I} / 3)}{4 \pi(\mathrm{a} / 2)} \sqrt{2}ight] \hat{\mathrm{k}} \
\overrightarrow{\mathrm{~B}}= & {\left[\frac{-2 \sqrt{2} \mu_0 \mathrm{I}}{3 \pi \mathrm{a}}+\frac{\sqrt{2} \mu_0 \mathrm{I}}{3 \pi \mathrm{a}}ight] \hat{\mathrm{k}} } \
\overrightarrow{\mathrm{~B}}= & \frac{-\sqrt{2} \mu_0 \mathrm{I}}{3 \pi \mathrm{a}} \hat{\mathrm{k}}
\end{aligned}$$

Answer

$\frac{2\mu_0 I}{3\pi a}$

Answer

$\frac{\sqrt{2}\mu_0 I}{3\pi a}$

Answer

$\frac{3\pi\mu_0 I}{\sqrt{2}a}$

Answer

$\frac{\mu_0 I}{2\pi a}$

Magnetism and Matter

Figure shows a current carrying square loop ABCD of edge length is ‘a’ lying in a plane. If the resistance of the ABC part is r and that of ADC part is 2r, then the magnitude of the resultant magnetic field at centre of the square loop is

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