Find charge inner/hollow sphere

In summary, using Gauss's Law and considering a gaussian surface with a radius between 3 and 5 cm, the charge on the inner sphere can be determined as -2400 x 4π(0.04)^2 = -3.04 x 10^-7 C. The charge on the hollow sphere can be determined as -300 x 4π(0.2)^2 = -7.54 x 10^-6 C.
  • #1
g98
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Homework Statement


A hollow conducting sphere with an inner radius of 5 cm and an outer radius of 6 cm contains a smaller sphere of radius 3 cm, located symmetrically inside the hollow sphere. The electric field strength at 4 cm from the center is measured to be 2400 N/C pointing inward. The electric field strength at 20 cm from the center is determined at 300 N/C pointing away from the spheres. Use this information to determine: a. the charge on the inner sphere b. the charge on the hollow sphere

Homework Equations

The Attempt at a Solution


I know I have to use the gauss's law but I am not quite sure how to do it
 
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  • #2
g98 said:

Homework Statement


A hollow conducting sphere with an inner radius of 5 cm and an outer radius of 6 cm contains a smaller sphere of radius 3 cm, located symmetrically inside the hollow sphere. The electric field strength at 4 cm from the center is measured to be 2400 N/C pointing inward. The electric field strength at 20 cm from the center is determined at 300 N/C pointing away from the spheres. Use this information to determine: a. the charge on the inner sphere b. the charge on the hollow sphere

Homework Equations

The Attempt at a Solution


I know I have to use the gauss's law but I am not quite sure how to do it
You have to show some attempt at solving the problem. What does Gauss' Law state?
 
  • #3
Consider first a gaussian surface of radius ##r## cm with ##3\lt r\lt 5##, and try to apply gauss's law. Also note that if ##Q## be the charge of the inner sphere, the inner surface of the spherical shell must have charge ##-Q##.
 
Last edited:

1. How do I calculate the charge of an inner/hollow sphere?

To calculate the charge of an inner/hollow sphere, you will need to know the radius of the sphere, the charge density, and the material the sphere is made of. Once you have this information, you can use the formula Q = 4πε0ρr3/3, where Q is the charge, ε0 is the permittivity of free space, ρ is the charge density, and r is the radius of the sphere.

2. Can the charge of an inner/hollow sphere be negative?

Yes, the charge of an inner/hollow sphere can be negative. The charge density of the sphere can be negative, resulting in a negative charge. This can occur if the material the sphere is made of has a negative charge or if there are more negative charges present than positive charges.

3. How does the charge distribution affect the electric field inside an inner/hollow sphere?

The charge distribution inside an inner/hollow sphere affects the electric field in two ways. First, the electric field will be zero at the center of the sphere due to the symmetry of the charge distribution. Second, the electric field will be non-zero near the surface of the sphere, and it will decrease as you move further away from the surface.

4. What is the difference between an inner and a hollow sphere in terms of charge distribution?

An inner sphere has charge distributed throughout its volume, while a hollow sphere has charge distributed only on its surface. This means that the charge density of an inner sphere will be higher than that of a hollow sphere, as the charge is spread out over a larger volume in the inner sphere.

5. How does the charge of an inner/hollow sphere affect its capacitance?

The charge of an inner/hollow sphere does not affect its capacitance. The capacitance of a sphere only depends on its radius and the permittivity of the material it is made of. However, the charge on the sphere will affect the electric field, which in turn can affect the capacitance of nearby objects.

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