An infinite number of point charges, each carrying $1 μ C$ charge, are placed along the y –axis at $y = 1 m, 2 m, 4 m, 8 m, .......$ . The total force on a 1 C point charge, placed at the origin, is $x \times 10^{3} N$ . The value of x, to the nearest integer, is ______
[ Take $\frac{1}{4 π ε_{0}} = 9 \times 10^{9} N m^{2} / C^{2}]$

Question

Infinity Learn · Accepted Answer

Let  $$q1=1C$$ and  $$q2=1$$μCForce 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 ⇒$$F=kq1q211$$−$$14=kq1q243$$⇒$$F=9$$×$$10911$$×$$10$$−$$643$$ ⇒$$F=12$$×$$103N$$

Electrostatic force

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Electrostatic force

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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]

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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