A point charge q = 1 μC is located at a distance 2 cm from one end of a thin insulating wire of length 10 cm having a charge Q = 24 μC, distributed uniformly along its length, as shown in figure. Force between q and wire i $s ____$ N.
(Use 1/(4πε₀) = 9 × 10⁹ N·m²/C²)

Question

A point charge q = 1 μC is located at a distance 2 cm from one end of a thin insulating wire of length 10 cm having a charge Q = 24 μC, distributed uniformly along its length, as shown in figure. Force between q and wire i $s ____$ N.

(Use 1/(4πε₀) = 9 × 10⁹ N·m²/C²)

G1 Physics · Accepted Answer

The wire has length L = 10 cm = 0.10 m and total charge Q = 24 μC. Hence its linear charge density is λ = Q/L = 24×10⁻⁶/0.10 = 2.4×10⁻⁴ C/m. Let x be the distance of an element dx from the point charge. The point charge is 2 cm from the nearer end, so x ranges from 0.02 m to 0.12 m. Charge on an element: dq = λdx. The force magnitude due to this element is dF = kq dq/x² = kqλ dx/x². Therefore, F = kqλ ∫ from 0.02 to 0.12 of dx/x² = kqλ[1/0.02 - 1/0.12]. Substitute: k = 9×10⁹, q = 1×10⁻⁶ C, λ =…

A point charge q = 1 μC is located at a distance 2 cm from one end of a thin insulating wire of length 10 cm having a charge Q = 24 μC, distributed uniformly along its length, as shown in figure. Force between q and wire i s ____ N. (Use 1/(4πε₀) = 9 × 10⁹ N·m²/C²)