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Chapter 23: Problem 36

Consider a proton to be a uniformly charged sphere 1 fm in radius. Find the electric energy density at the proton's surface.

Short Answer

Expert verified
The energy density at the surface of a proton can be calculated using the electric field and the permittivity of free space in the formula for electric energy density.

Step by step solution

01

Define Given Constants

Specify the constants in the problem. This includes the proton charge \(Q = 1.6 \times 10^{-19} C\), the permittivity of free space \(ε_0 = 8.85 \times 10^{-12} C^2/N \cdot m^2\) and the radius of the proton \(r = 1 \times 10^{-15} m\).
02

Calculate the Electric Field

Use Coulomb's Law to find the electric field \(E\) at the surface of the proton. The equation is \(E = \frac{Q}{4πε_0r^2}\). Substituting the values of Q, r, and \( ε_0 \) from step 1, calculate E.
03

Calculate the Energy Density

Now substitute \(E\) and \(ε_0\) into the formula for Energy Density \(u = \frac{ε_0E^2}{2}\) to find the energy density at the surface of the proton.

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Most popular questions from this chapter

A sphere of radius \(R\) contains charge \(Q\) spread uniformly throughout its volume. Find an expression for the electrostatic energy contained within the sphere itself. (Hint: Consult Example 21.1.)

A car battery stores about \(4 \mathrm{ M J }\) of energy. If this energy were used to create a uniform \(30-\mathrm{kV} / \mathrm{m}\) electric field, what volume would it occupy?

Which can store more energy: a \(1.0-\mu \mathrm{F}\) capacitor rated at \(250 \mathrm{V}\) or a 470 -pF capacitor rated at \(3 \mathrm{kV} ?\)

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