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 1C point charge, placed at the origin, is x × 103 N. The value of x, to the nearest integer, is __________. [Take (1)/(4πε₀) = 9 × 10⁹ Nm2/C2] Numerical answer type. Work it out, then open the answer.

Answer: 12. All forces on the charge at the origin act along the same line (along -y, repulsion). F = kq Q(1/1² + 1/2² + 1/4² +), a GP with ratio 1/4, sum = (1)/(1 - 1/4) = 4/3. F = 9 × 10⁹ × 10⁻⁶ × 1 × 4/3 = 12 × 10³ N So x = 12.

An infinite number of point charges, each carrying 1 μ C charge, are… | JEE Main 2021 (18 Mar, Shift 2)

Q59JEE Main 2021 · 18 MAR · SHIFT 2Medium

Electric Charge & Coulomb's Law

An infinite number of point charges, each carrying 1 $\mu$ C charge, are placed along the y-axis at y = 1 m, 2 m, 4 m, 8 m ...............

The total force on a 1C point charge, placed at the origin, is x $\times$ 103 N.

The value of x, to the nearest integer, is __________. [Take $\frac{1}{4\pi\varepsilon_0} = 9 \times 10^{9}$ Nm2/C2]

Numerical answer type. Work it out, then open the answer.

Show answer and solution

Answer: 12

All forces on the charge at the origin act along the same line (along $-y$ , repulsion).
$F = kq\,Q\left(\dfrac{1}{1^2} + \dfrac{1}{2^2} + \dfrac{1}{4^2} + \dots\right)$ , a GP with ratio $\tfrac{1}{4}$ , sum $= \dfrac{1}{1 - 1/4} = \dfrac{4}{3}$ .
$F = 9 \times 10^9 \times 10^{-6} \times 1 \times \dfrac{4}{3} = 12 \times 10^3\text{ N}$
So $x = 12$ .

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