The electric field at the surface of a uniformly charged sphere of radius 6.0cm is 90kN/C . What would be the field strength 10 cm from the surface?

To determine the electric field strength at a point outside a uniformly charged sphere, you can use Coulomb's law. Here's how you can calculate the electric field strength at a point 10 cm from the surface of the sphere:

1. Start by determining the electric field strength at the surface of the sphere. In this case, it is given as 90 kN/C.

2. Use the formula for the electric field strength of a point charge:

E = k * Q / r^2

where E is the electric field strength, k is Coulomb's constant (approximately 9 x 10^9 N*m^2/C^2), Q is the charge of the sphere, and r is the distance from the center of the sphere.

3. Since the sphere is uniformly charged, the charge Q can be calculated using the formula for the electric field strength at the surface of a sphere:

E = k * Q / R^2

where R is the radius of the sphere.

Rearrange the formula to solve for Q:

Q = E * R^2 / k

4. Calculate the charge of the sphere:

Q = (90,000 N/C) * (0.06 m)^2 / (9 x 10^9 N*m^2/C^2)

Q ≈ 3.6 x 10^-6 C

5. Now, apply Coulomb's law to find the electric field strength at a point 10 cm (0.1 m) from the surface. The distance from the center of the sphere to this point will be the sum of the sphere's radius and the distance from the surface:

r = R + d

where d is the distance from the sphere's surface (0.1 m in this case).

r = 0.06 m + 0.1 m

r = 0.16 m

Finally, calculate the electric field strength at this point using Coulomb's law:

E = k * Q / r^2

E ≈ (9 x 10^9 N*m^2/C^2) * (3.6 x 10^-6 C) / (0.16 m)^2

E ≈ 810 N/C

Therefore, the electric field strength at a point 10 cm from the surface of the uniformly charged sphere is approximately 810 N/C.