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Electrostatic Potential and Capacitance

  1. If potential (in volts) in a region is expressed as V(x, y, z) = 6 xy – y + 2yz, the electric field (in N/C) at point (1, 1, 0) is :
    1. -(6î + 5ĵ + 2̂k
    2. -(2î + 3ĵ + ̂k
    3. -(6î + 9ĵ + ̂k
    4. -(3î + 5ĵ + 3̂k
Correct Option: A

​Potential in a region ​
V = 6xy – y + 2yz ​As
we know the relation between electric potential and electric field is E = -dV/dX ​

E =
∂V
î +
∂V
ĵ +
∂V
̂k
∂x∂y∂z

E = [(6y î + (6x - 1 + 2z)ĵ + (2y)̂k]
E(1,1,0) = -( 6î + 5ĵ + 2̂k)



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