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Question

# For the electric field shown in figure, its vector representation will be

A
E=200 ^i2003 ^j
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B
E=100 ^i1003 ^j
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C
E=503 ^i1003 ^j
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D
E=10 ^i52 ^j
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Solution

## The correct option is A →E=200 ^i−200√3 ^jFrom the given diagram, the electric filed line are parallel and equally spaced. It means →E is uniform. The planes perpendicular to the direction of electric field represents an equipotential surface of 40 V, 20 V, & 0 V Potential difference between A and B ΔV=VA−VB=20 V ⇒ Distance between equipotential surfaces along direction of →E, d=(10 cm)cos30∘ ⇒d=0.1×√32 Therefore, we know that VA−VB=Ed ⇒20=E×0.1×√32 ⇒E=400√3 Now, component of electric field Ex=Ecos30∘ ^i ⇒Ex=(400√3×√32)^i=200 ^i Ey=−Esin30∘ ^j=−200√3 ^j ∴→E=200 ^i−200√3 ^j Therefore, option (a) is correct. Tip : Uniform electric field is characterized by equally spaced parallel field lines. For uniform electric field, we can apply ΔV=Ed, where d is the distance between two points along →E.

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