Question

A spherical conductor of radius 10 cm has a charge of 3.2 × 10⁻⁷C distributed

uniformly. What is the magnitude of electric field at a point 15cm from the centre of the sphere?
(1/4πϵ0 = 9 × 10⁹ Nm/C²)
A 1.28 × 10⁵N/C
B 1.28 × 10⁶N/C
C 1.28 × 10⁷N/C
D 1.28 × 10⁴N/C

Answer 1

The magnitude of the electric field at a point 15 cm from the center of the sphere is approximately 1.28 × 10⁵ N/C.

Step-by-step explanation:

To find the electric field at a point outside a spherical conductor with a distributed charge, we can use the formula:

E = k * (Q / r²)

Where:

• E is the electric field magnitude
• k is the electrostatic constant (1/4πϵ₀)
• Q is the charge of the conductor
• r is the distance from the center of the conductor

Plugging in the values given: Q = 3.2 × 10⁻⁷ C and r = 15 cm, we can calculate the electric field magnitude as follows:

E = (9 × 10⁹ Nm/C²) * (3.2 × 10⁻⁷ C / (0.15² m))

Simplifying the calculation, the magnitude of the electric field at a point 15 cm from the center of the sphere is approximately 1.28 × 10⁵ N/C.