Explanation As proton ’ s charge is spread uniformly throughout its volume. So, the electric field is same for all the regions of proton. Write the expression for the electrostatic energy within sphere. U 1 = K Q 2 10 R (I) Here, U 1 is the electrostatic energy within sphere, K is the constant, Q is the charge of proton, and R is the radius of proton. Write the expression for the electrostatic energy at the surface of sphere. U 2 = 1 2 ε 0 E 2 V (II) Here, U 2 is the electrostatic energy at the sphere, ε 0 is the permittivity of free space, E is the electric field, and V is the volume of sphere. Write the expression for the electric field at the surface of sphere. E = Q ε 0 A (III) Here, A is surface area of the sphere. Substitute Q ε 0 A for E in Equation (II) to find U . U 2 = 1 2 ε 0 ( Q ε 0 A ) 2 V (IV) Write the expression for total electrostatic energy within sphere and at the sphere. U = U 1 + U 2 (V) Here, U is the total electrostatic energy. Conclusion: Substitute 4 π R 2 for A , 4 3 π R 3 for V in Equation (IV) to find U 2 . U 2 = 1 2 ε 0 ( Q ε 0 4 π R 2 ) 2 4 3 π R 3 = Q 2 6 R ( 4 π ε 0 ) = K Q 2 6 R Substitute K Q 2 10 R for U 1 , K Q 2 6 R for U 2 in Equation (V) to find R

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Author: Wolfson, Richard

Publisher: Pearson Education,

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One of the fundamental properties is the electromagnetic property. Charge cannot be destroyed by any process and this contributes formally to the law of charge conservation.

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Chapter 23, Problem 36E

To determine

The radius of proton.

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Chapter 23, Problem 35E

Chapter 23, Problem 37P

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