Question

uniformly charged conducting sphere of 1.2 m diameter has surface charge density 8.1 mC/m2. Find (a) the net charge on the sphere and (b) the total electric flux leaving the surface.

Answer 1

Answer:

(a) = 3.7 × 10⁻⁵

(b) = 4.1 × 10⁻⁶ N.M²/C

Explanation:

(a) Diameter of the sphere, d = 1.2 m

Radius of the sphere, r = 0.6 m

Surface charge density, = 8.1 mC/m2 = 8.1 × 10⁻⁶ C/m²

Total charge on the surface of the sphere,

Q = Charge density × Surface area

    = 4πr²σ

   = 4 (3.14) (0.12²) (8.1 × 10⁻⁶)

   = 3.66 × 10⁻⁵C

   ≅ 3.7 × 10⁻⁵C

Therefore, the net charge on the sphere is  3.7 × 10⁻⁵C

(b)

Total electric flux (∅)

=Q / ε₀

ε₀ =  8.854 × 10⁻¹² N⁻¹C² m⁻²

Q =   3.66 × 10⁻⁵C

 =  3.66 × 10⁻⁵ / 8.854 × 10⁻¹²

= 4.1 × 10⁻⁶ N.M²/C