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QPages 121-124: Q60: HC Verma: Concepts of Physics - Volume 2 Electric Field Potential Pages 121-124: Q60 Solution: The electric potential existing in space is . a) Write the…

⚠️ Common Exam Traps & Conceptual Pitfalls

When computing the electric field components via $\vec{E} = -\nabla V$, ensure you correctly identify all terms containing the specific coordinate variable (e.g., both $xy$ and $zx$ contribute to $E_x$) rather than isolating only the primary diagonal term. This prevents missing cross-terms that significantly alter the final magnitude calculation.

The electric potential existing in space is Vx,y,z)=Axy+yz+zx)Vx,y,z) = Axy + yz + zx). a) Write the dimensional formula of A. b) Find the expression for the electric field. c) If A is 10 SI units, find the magnitude of the electric field at 1 m, 1 m, 1 m).1 m, 1 m, 1 m).

Step-by-Step Verified Solution

**Answer:** (a) [A] = [M L_ T__ A__] (b) E⃗=−A(y+z)i^−A(x+z)j^−A(x+y)k^\vec{E} = -A(y+z)\hat{i} - A(x+z)\hat{j} - A(x+y)\hat{k} (c) E=34.6E = 34.6 V/m. **STEP-BY-STEP Explanation:** (a) V=A(xy+yz+zx)V = A(xy + yz + zx). Since VV has dimensions V, [A] = [V]/[L_] = [M L_ T__ A__]. (b) E⃗=−∇V\vec{E} = -\nabla V. (c) At (1,1,1): E=A(1+1)2+(1+1)2+(1+1)2=1012=34.6E = A\sqrt{(1+1)^2 + (1+1)^2 + (1+1)^2} = 10\sqrt{12} = 34.6 V/m .

All Questions in this Chapter

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