Potential Gradient and Relation between Electric Field and Potential
In a space, p...
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 (6,6√3)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 C210∘ 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 (6,6√3) tanθ=EyEx=−1y−1x=xy=66√3=1√3
As θ is in third quadrant
Angle between →E and X axis is =180+30=210o