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If the equation of an electric field is ...

If the equation of an electric field is `vec(E ) = (y hat(i) + xhat(j))`, then the equation of electric potential is represented by

A

`V = -(x+y) + "constant"`

B

`C = "constant"`

C

`V = -(x^(2)+y^(2))+"constant"`

D

`V = -xy + "constant"`

Text Solution

Verified by Experts

The correct Answer is:
D
Hint: We know that
`dV = vec(E ) cdot dvec(r ) = -(y hat(i)+xhat(j))(hat(i)dx+hat(j)dy+hat(k)dz)`
`=-(ydx+xdy) = -d(xy)`
Integrating, we get
`V = -xy` + constant
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