Q.

An infinite number of point charges, each carrying  1μC charge, are placed along the y –axis at  y=1 m, 2m,4m,8m,........ The total force on a 1 C point charge, placed at the origin, is x×103N . The value of x, to the nearest integer, is ______[ Take14πε0=9×109Nm2/C2]

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answer is 12.

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Detailed Solution

Let  q1=1C and  q2=1μCForce on 1C charge due to infinite charges can be written as F=kq1q21+122+142+182+....Sum of infinite GP = a1-r here a= first term and r =common ratio ⇒F=kq1q211−14=kq1q243⇒F=9×10911×10−643 ⇒F=12×103N
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An infinite number of point charges, each carrying  1μC charge, are placed along the y –axis at  y=1 m, 2m,4m,8m,........ The total force on a 1 C point charge, placed at the origin, is x×103N . The value of x, to the nearest integer, is ______[ Take14πε0=9×109Nm2/C2]