Question

In: Physics

a nonconducting thin spherical shell of radius 6.00 cm has a uniform density of 9.00 nC/m^2....

a nonconducting thin spherical shell of radius 6.00 cm has a uniform density of 9.00 nC/m^2.
a. what is the total charge on the shell
b. what is the electric field at a distance of 2.00 cm from the center of the shell?
c. what is the electric field a distance 10.0 cm from the center of the shell.

Expert Solution

a.

The radius of the thin spherical shell is

r = 6.00 cm

The surface area of the thin spherical shell is

A = 4r²

Charge desnity of the ono conducting thin spherical shell is

= 9.00 nC/m²

Now, the total charge on the shell is

Q = A

= 4r²

Substitute 6.00 cm for r and 9.00 nC/ m² for in the above equation,

Rounding off to three significant figures, the total charge on the thin spherical shell is 4.07 x 10^-10 C.

b.

The electric field at any points inside a thin spherical shell is always zero.

As the distance 2.00 cm from the centre of the spherical shell lies inside it, the electric field is zero.

Therefore, the electric field at a distance of 2.00 cm from the center of the shell is zero.

c.

The electric field outside the thin spherical shell at a point x from its center is

Here, permittivity of free space is ₀.

Substitute 4.07 x 10-10 C for Q, 1.25663706 × 10^-6 m kg /s² A² for ₀ and 10.0 cm for x in the above equation,

Rounding off to three significant figures, the electric field a distance 10.0 cm from the center of the thin spherical shell is 3.66 x 10² N/C.

genius_generous answered 1 hour ago

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