Question

A charged ring with a radius of 60 cm is located with its center at the origin and the plane of the ring perpendicular to the x axis. At x = 48 cm, the electric field of a charged ring is 4.83 x 104 N/C. What is the total charge of the ring?

Answer 1

The total charge of a ring which will be given by -

E = k Q_total / d²

E = k Q_total / (x² + R²)

where, k = proportionality constant = 9 x 10⁹ Nm²/C²

E = electric field of a charged ring = 4.83 x 10⁴ N/C

R = radius of a charged ring = 0.6 m

x = horizontal distance = 0.48 m

then, we get

(4.83 x 10⁴ N/C) = (9 x 10⁹ Nm²/C²) Q_total / [(0.48 m)² + (0.6 m)²]

(4.83 x 10⁴ N/C) = (9 x 10⁹ Nm²/C²) Q_total / (0.5904 m²)

Q_total = [(4.83 x 10⁴ N/C) (0.5904 m²)] / (9 x 10⁹ Nm²/C²)

Q_total = [(28516.32 Nm²/C) / (9 x 10⁹ Nm²/C²)]

Q_total = 3.16 x 10^-6 C

Q_total = 3.16 C