Concepts Of Physics MCQ Edition [Volume 2]PhysicsElectric Field and Potential
The electric potential in a region of space is described by V(x, y, z) = A(xy + yz + zx) . Find the expression for the electric field.
Options
- A-A i (x) + j (y) + k (z)
- B-A i (y + z) + j (z + x) + k (x + y)
- CA i (y + z) + j (z + x) + k (x + y)
- D-A i (yz) + j (zx) + k (xy)
Correct answer
B. -A i (y + z) + j (z + x) + k (x + y)
Step-by-step solution
The electric field E is related to the electric potential V by the negative gradient of the potential: E = - V = - ( V x i + V y j + V z k ) Given V(x, y, z) = A(xy + yz + zx) Calculating the partial derivatives: V x = A(y + z) V y = A(x + z) V z = A(y + x) Substituting these into the expression for the electric field: E = -A (y + z) i + (z + x) j + (x + y) k E = -A i (y + z) + j (z + x) + k (x + y)