Question

A uniformly charged conducting sphere of 1.22m radius has a surface charge density 8.13µCm-2.
(a) Find the charge on sphere
(b) What is the total electric flux leaving surface of sphere?
(c) Calculate electric field at surface of sphere

Answer 1

(a) The magnitude of the charge on sphere is 1.52 x 10⁻⁸ C.

(b) The total electric flux leaving surface of sphere is 1,717.86 Nm²/C.

(c) The electric field at surface of sphere is 91.82 N/C.

Charge on sphere

The charge on the sphere is calculated as follows;

Q = Aσ

where;

• A is area of the sphere

A = 4πr²

A = 4π(1.22)² = 18.7 m²

Q = (18.7) x (8.13 x 10⁻⁶ x 10⁻⁴)

note: 1 cm² = 10⁻⁴ m²

Q = 1.52 x 10⁻⁸ C

Total electric flux

Ф = Q/ε₀

Φ = (1.52 x 10⁻⁸) / (8.85 x 10⁻¹²)

Φ  = 1,717.86 Nm²/C

Electric field at surface of the sphere

E = Ф/A

$E = \frac{Q}{4\pi \varepsilon _0 r^2} \\\\E = \frac{1.52 \times 10^{-8} }{4\pi \times 8.85 \times 10^{-12} \times (1.22)^2} \\\\E = 91.82 \ N/C$

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