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Moving Charges and Magnetism — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsMoving Charges and Magnetism5 Marks
Question
A rectangular conducting loop consists of two wires on two opposite sides of length l joined together by rods of length d. The wires are each of the same material but with cross-sections differing by a factor of 2. The thicker wire has a resistance R and the rods are of low resistance, which in turn are connected to a constant voltage source $V_0.$ The loop is placed in uniform a magnetic field B at 45° to its plane. Find $\tau$, the torque exerted by the magnetic field on the loop about an axis through the centres of rods.
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Answer


Torque on the first wire is given by,
$\text{F}_1=\text{i}_1\text{lB}=\frac{\text{V}_0}{\text{R}}\text{lB},\tau_1=\frac{\text{d}}{2\sqrt{2}}\text{F}_1=\frac{\text{V}_0\text{ldB}}{4\sqrt{2}\text{R}}$
Torque on the second wire is given by,
$\text{F}_2=\text{i}_2\text{lB}=\frac{\text{V}_0}{2\text{R}}\text{lB},\tau_2=\frac{\text{d}}{2\sqrt{2}}\text{F}_2=\frac{\text{V}_0\text{ldB}}{4\sqrt{2}\text{R}}$
Net torque, $\tau=\tau_1-\tau_2$
$\Rightarrow\ \tau=\frac{1}{4\sqrt{2}}\frac{\text{V}_0\text{AB}}{\text{R}}.$

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