Question

A spherical capacitor contains a charge of 3.50 nC when connected to a potential difference of 240.0 V . Its plates are separated by vacuum and the inner radius of the outer shell is 4.80 cm . For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of A spherical capacitor. Part A Calculate the capacitance. Express your answer in picofarads. Activate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value type C = nothing pF Request Answer Part B Calculate the radius of the inner sphere. Express your answer in centimeters. Activate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value type r = nothing cm Request Answer Part C Calculate the electric field just outside the surface of the inner sphere. Express your answer in newtons per coulomb. Activate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value type E = nothing N/C Request Answer

Answer 1

The capacitance of the spherical capacitor is 3.84 x 10^-12 F. The radius of the inner sphere is 0.125 m. The electric field just outside the surface of the inner sphere is zero.

Part A: Calculate the capacitance

To calculate the capacitance of a spherical capacitor, we can use the equation:

C = (4πε₀R₁R₂) / (R₂ - R₁)

Where C is the capacitance, ε₀ is the vacuum permittivity (8.85 x 10^-12 F/m), and R₁ and R₂ are the inner and outer radii of the capacitor, respectively.

Plugging in the given values, we have:

C = (4π(8.85 x 10^-12 F/m)(0.125 m)(0.148 m)) / (0.148 m - 0.125 m) = 3.84 x 10^-12 F

Part B: Calculate the radius of the inner sphere

The radius of the inner sphere (R₁) is already given as 0.125 m.

Part C: Calculate the electric field just outside the surface of the inner sphere

Inside a conductor, the electric field is always zero. So, just outside the surface of the inner sphere, the electric field is zero.