Concept explainers
(a)
The electric potential of each sphere.
(a)
Answer to Problem 31P
The electric potential of each sphere is
Explanation of Solution
The potential on each sphere will be same.
Write the equation at same potential.
Here,
Write the expression for the potential larger sphere.
Here,
Write the expression for the potential for smaller sphere.
Here,
Rewrite the expression for the potential from equation (I) by using (II) and (III).
Write the expression for total charge by using (IV).
Conclusion:
Substitute,
Substitute,
Substitute,
The sphere is having same potential.
Thus, the electric potential of each sphere is
(b)
The electric field at the surface of each sphere.
(b)
Answer to Problem 31P
The electric fields at the surface of each sphere are
Explanation of Solution
Write the equation electric field for larger sphere.
Here,
Write the equation electric field for smaller sphere.
Here,
Conclusion:
Substitute,
Substitute,
Thus, the electric fields at the surface of each sphere are
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Chapter 20 Solutions
Principles of Physics: A Calculus-Based Text
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