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NEET 2014 (AIPMT) · Electric Potential & Equipotentials

Electric Potential & Equipotentials question from NEET 2014 (AIPMT)

Q107NEET 2014 · AIPMTMedium

Electric Potential & Equipotentials

In a region, the potential is represented by V(x, y, z) = 6x −- 8xy −- 8y + 6yz, where VV is in volts and x, y, z are in metres. The electric force experienced by a charge of 2 coulomb situated at point (1, 1, 1) is

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Answer: (d)

  1. E⃗=−∇V\vec{E} = -\nabla V: Ex=−(6−8y)E_x = -(6 - 8y), Ey=−(−8x−8+6z)E_y = -(-8x - 8 + 6z), Ez=−6yE_z = -6y.
  2. At (1,1,1)(1,1,1): E⃗=2i^+10j^−6k^\vec{E} = 2\hat{i} + 10\hat{j} - 6\hat{k}, ∣E⃗∣=4+100+36=235 V/m|\vec{E}| = \sqrt{4 + 100 + 36} = 2\sqrt{35}\,\text{V/m}.
  3. F=qE=2×235=435 NF = qE = 2\times 2\sqrt{35} = 4\sqrt{35}\,\text{N}
  4. So the answer is (d) 4354\sqrt{35} N.
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