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The electric field in a space E → = 4 i ^ - 5 k ^ V m - 1 . What is the potential difference V B - V A between points A and B ? The coordinates of A and B are 4 , 0 , 3 m and 10 , 3 , 0 m , respectively.

Options

  1. A- 39   V
  2. B11   V
  3. C25   V
  4. D-25   V

Correct answer

A. - 39   V

Step-by-step solution

Since, we know, V 2 - V 1 = - ∫ r 1 r 2 E → ⋅ d r Given, E → = 4 i ^ - 5 k ^   V   m - 1 , A → = 4 i ^ + 3 k ^ and B → = 10 i ^ + 3 j ^ ∴   Potential difference = V B - V A Putting given values, we get =   - ∫ r A r B 4 i ^ - 5 k ^ ⋅ dx i ^ + dr j ^ + dz k ^ =   - ∫ 4 ,   0 ,   3 10 ,   3 ,   0 4 d x - 5 d z = - 4 x 4 10 - 5 z 3 0 = - 39   V

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