Question

# A uniform electric field having strenght is existing in x-y plane as shown in figure. Find the p.d. between origin O & A (d,d,0),

A
Ed(cosθ+sinθ)
B
Ed(sinθcosθ)
C
2Ed
D
None of these
Solution
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#### When the electric field E in x-y plane makes angle θ with the x-axis , the electric filed can be written as →E=Ecosθ^i+Esinθ^jThus, Ex=Ecosθ , Ey=Esinθ and Ez=0Since →E=−→∇VdrSo, dVx=−Exdx, dVy=−Eydy and dVz=−EzdzNow ingratiating, Vx=−∫0dEcosθdx=−Ecosθ(0−d)=Edcosθ Vy=−∫0dEsinθdy=−Esinθ(0−d)=Edsinθand Vz=0Thus, potential between O and A is V=Vx+Vy+Vz=Edcosθ+Edsinθ

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