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Question

Electric potential in a region is varying according to the relation V=3x22y24 , where x and y are in meter and V is in volt. Electric field intensity in N/C at a point (1 m, 2 m) is

A
3^i^j
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B
3^i+^j
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C
6^i2^j
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D
6^i+2^j
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Solution

The correct option is B 3^i+^j
Electric potential, V=3x22y24

Relation between electric potential and electric field intensity is given by,

E=[Vx^i+Vy^j+Vz^k]....(1)

Now,

Vx=(3x22y24)x=3x

Similarly,

Vy=y2 and Vz=0

From (1) equation, we have

E=3x^i+y2^j

At point (1 m,2 m)

E=(3×1)^i+22^j
E=3^i+^j

Hence, option (b) is the correct answer.

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