Q.

Infinite number of charges each of magnitude 2C are placed on x-axis at 1m, 2m, 4m, ..... from origin along +ve x-axis.  The first charge is positive and alternate charges are of opposite in nature.  The electric field intensity at the origin

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a

110 π ∈0  along  +ve  x−axis

b

25 π ∈0  along  −ve  x−axis

c

1 π ∈0  along  +ve  x−axis

d

1 π ∈0  along  −ve  x−axis

answer is B.

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Detailed Solution

Enet=E1+E2+E3+E4+...... =kQr12-kQr22+kQr32-kQr42+.... =kQ1r12-1r22+1r32-.....=k2112-122+132-..... =24π∈0[11+14]=24π∈0×45=25π∈0∵S∞=a1-r, here a =1, r=t2t1=-1221=-14
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