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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),
119723_b46138f6c280477d978109375631aa2d.png
  1. Ed(cosθ+sinθ)
  2. Ed(sinθcosθ)
  3. 2Ed
  4. None of these

A
Ed(sinθcosθ)
B
2Ed
C
Ed(cosθ+sinθ)
D
None of these
Solution
Verified by Toppr

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^j
Thus, Ex=Ecosθ , Ey=Esinθ and Ez=0
Since E=Vdr
So, dVx=Exdx, dVy=Eydy and dVz=Ezdz
Now ingratiating, Vx=0dEcosθdx=Ecosθ(0d)=Edcosθ
Vy=0dEsinθdy=Esinθ(0d)=Edsinθ
and Vz=0
Thus, potential between O and A is V=Vx+Vy+Vz=Edcosθ+Edsinθ

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