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

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 $\frac{1}{4 π ϵ_{0}} = 9 \times 10^{9} N m^{2} C^{- 2}$ ]

Aicharya · Accepted Answer

F = k 1 &#160; C 1 &#160; &#956; C 1 + 1 2 2 + 1 4 2 + 1 8 2 + &#8230; = 9 &#215; 10 3 1 1 - 1 4 = 12 &#215; 10 3 &#160; N

An infinite number of point charges, each carrying 1   μ C charge, are placed along the y-axis at…