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Question

The gravitational field in a region is given by E=(2i + 3j)N kg1. Show that no work is done by the gravitational field when a particle is moved on the line 3y+2x=5.

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Solution

Electric field acts in direction when slope is m1=32
But slope of the line 3y+2x=5 is m2=23
Force is along the direction of field ,(m1×m2=(32×23)=1
Angle between electric filed direction and displacement direction is,
tanθ=m1m21+m1m2=
θ=90
Since θ=90 ,no work is done by the field.

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