Assertion : The magnetic field at the centre | vedclass

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(D) The magnetic field at the center of a circular arc of radius $R$ carrying current $I$ and subtending an angle $\phi$ at the center is given by $B

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If both the Assertion and Reason are incorrect.

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(D) The magnetic field at the center of a circular arc of radius $R$ carrying current $I$ and subtending an angle $\phi$ at the center is given by $B = \frac{\phi}{2\pi} \cdot \frac{\mu_0 I}{2R}$.For the given coil,the current $I$ splits into $I_1$ and $I_2$ along arcs subtending angles $	heta$ and $(2\pi - 	heta)$ respectively.The magnetic field due to arc $I_1$ is $B_1 = \frac{	heta}{2\pi} \cdot \frac{\mu_0 I_1}{2R}$ (directed into the page).The magnetic field due to arc $I_2$ is $B_2 = \frac{2\pi - 	heta}{2\pi} \cdot \frac{\mu_0 I_2}{2R}$ (directed out of the page).For the net magnetic field to be zero,$B_1 = B_2$,which implies $	heta I_1 = (2\pi - 	heta) I_2$.This condition is not satisfied simply by $I_1 = I_2$ unless $	heta = \pi$ (i.e.,the currents split into two semicircles). Therefore,the Assertion is generally false,and the Reason is also incorrect as $I_1 = I_2$ does not guarantee zero field unless the geometry is symmetric.

Assertion : The magnetic field at the centre of the circular coil in the following figure due to the currents $I_1$ and $I_2$ is zero.
Reason : $I_1 = I_2$ implies that the fields due to the current $I_1$ and $I_2$ will be balanced.

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Assertion : The magnetic field at the centre of the circular coil in the following figure due to the currents $I_1$ and $I_2$ is zero.Reason : $I_1 = I_2$ implies that the fields due to the current $I_1$ and $I_2$ will be balanced.