Equipotential surfaces are shown in figure. Then the electric field strength will be

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  1. 100 Vm−1 along X-axis
  2. 100 Vm−1 along Y-axis
  3. 200 Vm−1 at an angle 120 ∘ with X-axis
  4. 50 Vm−1at an angle 120 ∘ with X-axis 

Answer (Detailed Solution Below)

Option 3 : 200 Vm−1 at an angle 120 ∘ with X-axis
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Detailed Solution

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Concept:

Electric field strength is perpendicular to the equipotential surface and is given by the negative gradient of the potential.

Electric field strength, E = - (dV / dx)

Calculation:

Given the potential difference between the equipotential surfaces is 10 V and the distance between them is 0.05 m.

⇒ E = - (10 / 0.05)

⇒ E = - 200 V/m

The direction of the electric field is perpendicular to the equipotential surfaces and towards decreasing potential.

Given that the angle with the X-axis is 120°.

Hence, the electric field strength is 200 V/m at an angle 120° with the X-axis.

∴ The correct answer is option 3.

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