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Question

In a space, potential (V) is given by V=loge(xy), where V,x,y are in SI units. The angle between E & X-axis at point (6,63)m

A
30
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B
150
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C
210
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D
240
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Solution

The correct option is C 210
Electric field is defined as E=dVdr
Electric field along x-axis
Ex=ddx{logex+logey}=1x
Electric field along y-axis
Ey=ddy{logex+logey}=1y

(Ex,Ey)=(1x,1y)



As (x,y) is (6,63)
tanθ=EyEx=1y1x=xy=663=13

As θ is in third quadrant
Angle between E and X axis is
=180+30=210o

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