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Question

Find the net electric field due to a finite wire of linear charge density +λ C/m at a point P located at a perpendicular distance d as shown in the figure.

[K=14πε0]


A
2Kλd
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B
22Kλd
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C
Kλ2d
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D
122Kλd
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Solution

The correct option is A 2Kλd

We know that electric field intensity (Eperp) perpendicular to the uniformly charged wire at distance d is,

Eperp=Kλd[sin θ1+sin θ2]

According to problem,

θ1=30 and θ2=60

Substituting the values in the above equation, we get

Eperp=Kλd[sin30+sin60]

Eperp=Kλd[12+32]

Eperp=Kλd[3+12]

Electric field intensity (Epara) parallel to the uniformly charged wire at distance d is,

Epara=Kλd[cosθ1cosθ2]

Substituting the values of θ1 and θ2, we get,

Epara=Kλd[cos30cos60]

Epara=Kλd[12+32]

Epara=Kλd[1+32]

Now, net electric field intensity at point P,

Enet=(Epara)2+(Eperp)2

Enet= (Kλd)2(1+32)2+(1+32)2

Enet=Kλ2d(1+3)2+(1+3)2

Enet=Kλ2d4+4

Enet=2Kλd

Hence, option (a) is the correct answer.

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