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NEET 2015 (AIPMT) · Electric Potential & Equipotentials

Electric Potential & Equipotentials question from NEET 2015 (AIPMT)

Q103NEET 2015 · AIPMTEasy

Electric Potential & Equipotentials

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

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Answer: (d)

  1. E⃗=−(∂V∂xi^+∂V∂yj^+∂V∂zk^)\vec{E} = -\left(\frac{\partial V}{\partial x}\hat{i} + \frac{\partial V}{\partial y}\hat{j} + \frac{\partial V}{\partial z}\hat{k}\right)
  2. ∂V∂x=6y=6\frac{\partial V}{\partial x} = 6y = 6, ∂V∂y=6x−1+2z=5\frac{\partial V}{\partial y} = 6x - 1 + 2z = 5, ∂V∂z=2y=2\frac{\partial V}{\partial z} = 2y = 2 at (1,1,0)(1,1,0)
  3. E⃗=−(6i^+5j^+2k^)\vec{E} = -(6\hat{i} + 5\hat{j} + 2\hat{k})
  4. So the answer is (d).
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