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JEE Main 2017 (8 Apr, Shift 1) · Electric Potential & Equipotentials

Electric Potential & Equipotentials question from JEE Main 2017 (8 Apr, Shift 1)

Q100JEE Main 2017 · 8 APR · SHIFT 1Medium

Electric Potential & Equipotentials

There is a uniform electrostatic field in a region. The potential at various points on a small sphere centred at P,P, in the region, is found to vary between the limits 589.0 V to 589.8 V. What is the potential at a point on the sphere whose radius vector makes an angle of 60o with the direction of the field?

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Answer: (c)

  1. In a uniform field V=VP−Ercos⁡θV = V_P - Er\cos\theta on the sphere, θ\theta measured from the field direction.
  2. Max 589.8589.8 at θ=180∘\theta = 180^\circ, min 589.0589.0 at θ=0\theta = 0: VP=589.4 VV_P = 589.4\,\text{V}, Er=0.4 VEr = 0.4\,\text{V}.
  3. At θ=60∘\theta = 60^\circ: V=589.4−0.4cos⁡60∘=589.4−0.2=589.2 VV = 589.4 - 0.4\cos 60^\circ = 589.4 - 0.2 = 589.2\,\text{V}
  4. So the working gives (b) 589.2 V.
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