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 × 10

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

TestHub · Accepted Answer

F = k 1 C 1 μ C 1 + 1 2 2 + 1 4 2 + 1 8 2 + … = 9 × 10 3 1 1 - 1 4 = 12 × 10 3 N

Physics - Electrostatics Question with Solution | TestHub