If the potential in a region is given by the function V = 2 x − y 2 − cos(z), what is the y-component of the electric field at the point P = (x ′ , y ′ , z ′ )?

2y

Explanation:

Electric field in terms of Electric potential is given as:

E = dV/dr(x, y, z)

Where r(x, y, z) = position in x, y, z plane

The y component of the Electric field will be:

Ey = -dV/dy

Given that

V = 2x - y² - cos(z)

dV/dy = -2y

=> E = - (-2y)

E = 2y

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