If potential (in volts) in a region is expressed as V(x, y, z) = 6xy - y + 2yz, the electric field (in N/C) at (1,1,0) is:
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Question

If potential (in volts) in a region is expressed as V(x,y,z) = 6xy − y + 2yz, the electric field (in N/C) at (1,1,0) is:

G1 Physics · Accepted Answer

Step 1: Electric field E⃗ = −∇V. Step 2: Eₓ = −∂V/∂x = −6y; Eᵧ = −∂V/∂y = −(6x −1 +2z); E𝓏 = −∂V/∂z = −2y. Step 3: At (1,1,0), E⃗ = −6î −5ĵ −2k̂.