Calculation of Maximum Electric Field Due to Sphere

Given:
Radius of sphere, r = 10 cm = 0.1 m
Charge on sphere, Q = 1 µC = 10^-6 C

Formula for Electric Field Due to a Sphere

The formula for electric field due to a sphere at a distance r from its center is given by:

E = kQ/r^2

where k is the Coulomb’s constant, which is equal to 9 x 10^9 N.m^2/C^2.

Calculation of Maximum Electric Field

To calculate the maximum electric field due to the sphere, we need to find the distance from the center of the sphere where the electric field will be maximum. This distance is equal to the radius of the sphere, i.e., r = 0.1 m.

Now, we can substitute the values of Q, r, and k in the formula to get the maximum electric field:

E = kQ/r^2
E = (9 x 10^9 N.m^2/C^2) x (10^-6 C) / (0.1 m)^2
E = 9 x 10^5 N/C

Therefore, the maximum electric field due to the sphere is 9 x 10^5 N/C.

Explanation

When a charged object is placed in an electric field, it experiences a force due to the electric field. The electric field is a vector quantity that is defined at every point in space. The direction of the electric field is the direction in which a positive test charge would move if placed in the field.

In the case of a charged sphere, the electric field at a point outside the sphere is radial and is directed away from the center of the sphere. The magnitude of the electric field at a distance r from the center of the sphere is given by the formula E = kQ/r^2, where k is the Coulomb’s constant, Q is the charge on the sphere, and r is the distance from the center of the sphere.

The maximum electric field due to the sphere occurs at a distance equal to the radius of the sphere. This is because the electric field is a function of distance from the center of the sphere and is maximum at the surface of the sphere.