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Question

The equation of an equipotential line in an electric field is y=2x, then the electric field strength vector at (1,2) may be :
  1. 4^i+3^j
  2. 4^i+8^j
  3. 8^i+4^j
  4. 8^i+4^j

A
4^i+8^j
B
8^i+4^j
C
4^i+3^j
D
8^i+4^j
Solution
Verified by Toppr

Now equation of equipotential surface is y=2x
Now electric field along the euipotential surface should be zero
therefore angle made by equipotential surface with x-axis is tan1(2)
Now since net electric field should be perpendicular to the equipotential surface
therefore for any electric field which makes an angle tan1(1/2) with x-axis can be the electric field at point (1,2) which is true only for option (D)
because for two perpendicular line, product of their slope should be equal to -1 i.e., m1×m2=1

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