Air becomes a conductor when the electric field strength exceeds 3.01 * 106 N/C. Determine the maximum amount of charge that can be carried by a metal sphere 5.0 m in radius. The value of the Coulomb constant is 8.99 * 109 N · m2 / C 2. Answer in units of C.

8.37*10⁻³ C.

Explanation:

The formula of electric field is given as

E = kq/r² ... Equation 1

Where E = electric field, q = amount of charge, k = coulomb constant, r = radius of the sphere

make q the subject of the equation

q = Er²/k ... Equation 2

Given: E = 3.01*10⁶ N/C, r = 5.0 m, k = 8.99*10⁹ Nm²/C².

Substitute into equation 2

q = (3.01*10⁶) (5²) / (8.99*10⁹)

q = (75.25/8.99) * 10⁻³

q = 8.37*10⁻³ C.

Hence the maximum amount of charge = 8.37*10⁻³ C.