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JEE MainPhysicsElectrostatics

A point charge Q is placed at the origin (0, 0, 0) of a 3D coordinate system. Two points A and B are located at (2, 3, 3 ) m and (x, 5 , 2 ) m respectively. If the work done in moving a test charge from point A to point B is zero, the positive value of the unknown coordinate x is:

Options

  1. A4 m
  2. B3 m
  3. C9 m
  4. D5 m

Correct answer

B. 3 m

Step-by-step solution

The work done in moving a test charge from point A to point B is zero, which implies that the potential difference between the two points is zero. Thus, both points must lie on the same equipotential surface, meaning they are at the same distance from the origin. The distance of point A from the origin is: r_A = 2^2 + 3^2 + ( 3 )^2 = 4 + 9 + 3 = 16 = 4 m The distance of point B from the origin is: r_B = x^2 + ( 5 )^2 + ( 2 )^2 = x^2 + 5 + 2 = x^2 + 7 m Equating the distances: r_A = r_B 4 = x^2 + 7 16 = x^2 + 7 x^2

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