The charge Q = πC is distributed on a thin semicircular ring of radius R = 2m. There is a uniform electrostatic field $\left\vert\vec{E}\right\vert$ = 2N C⁻¹ directed horizontally. The semicircular ring can rotate freely about a fixed vertical axis AB. Initially the ring is in static equilibrium as shown in figure. If we want to rotate it about the fixed axis by 90° then minimum work required on the ring is x J. Find the value of x.
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Question

The charge Q = πC is distributed on a thin semicircular ring of radius R = 2m. There is a uniform electrostatic field $\left\vert\vec{E}\right\vert$ = 2N C⁻¹ directed horizontally. The semicircular ring can rotate freely about a fixed vertical axis AB. Initially the ring is in static equilibrium as shown in figure. If we want to rotate it about the fixed axis by 90° then minimum work required on the ring is x J. Find the value of x.

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G1 Physics · Accepted Answer

Step 1: Identify the relevant electrostatic principle—Coulomb's law, superposition, Gauss's law, potential-energy conservation or conductor boundary conditions. Step 2: Write the corresponding equation using the quantities in the question and simplify the geometry. Step 3: Substitute the given values and compare with the alternatives. Final: 8.