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Moving Charges And Magnetism

Question
CBSEENPH12039629

The potential at a point x (measured in µm) due to some changes situated on the x-axis is given by V (x) = 20 /x2- 4) volts. The electric field E at x = 4 µm is given by

  • 5/3 Volt/µm and in the –ve x direction

  • 5/3 Volt/µm and in the +ve x direction

  • 10/9 Volt/µm and in the -ve x direction

  • 10/9 Volt/µm and in the +ve x direction

Solution

D.

10/9 Volt/µm and in the +ve x direction

straight V subscript straight x space equals space fraction numerator 20 over denominator straight x squared minus 4 end fraction
straight E space equals space minus space dV over dx space equals space fraction numerator 20 over denominator left parenthesis straight x squared minus 4 right parenthesis squared end fraction space left parenthesis 2 straight x minus 0 right parenthesis space equals space 160 over 144 space equals space 10 over 9