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Question

# Determine the electric field strength vector if the potential of this field depends on x,y coordinates as V=10axy.

A
10a(y^i+x^j)
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B
10a(y^i+x^j)
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C
10a(x^j+y^k)
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D
a(y^i+x^j)
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Solution

## The correct option is B −10a(y^i+x^j)Given, Electric potential , V=10axy Relation between electric field vector and electric potential at any point is given by, →E=−[∂V∂x^i+∂V∂y^j+∂V∂z^k]....(1) Now, ∂V∂x=∂(10axy)∂x=10ay ∂V∂y=∂(10axy)∂y=10ax ∂V∂z=∂(10axy)∂z=0 Substituting the values in equation (1) we get, →E=−(10ay^i+10ax^j+0^k) ∴→E=−10a(y^i+x^j+0^k) Hence, option (b) is the correct answer.

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