For a cylindrical capacitor, as the outer radius B becomes much larger than the inner radius A, the factor ln(B/A) grows. What is the qualitative effect on the capacitance C = 2π ε0 L / ln(B/A)?

For a cylindrical capacitor, as the outer radius B becomes much larger than the inner radius A, the factor ln(B/A) grows. What is the qualitative effect on the capacitance C = 2π ε0 L / ln(B/A)?

• A. C increases
• B. C decreases
• C. C remains the same
• D. C becomes negative

Answer: (B)

Capacitance in a coaxial cylinder depends on the logarithm of the radius ratio, through C = 2π ε0 L / ln(B/A). With the inner radius A fixed, increasing the outer radius B makes the ratio B/A larger, so ln(B/A) grows. Since the numerator (2π ε0 L) is fixed for a given length, a larger denominator means a smaller capacitance. In the extreme where B becomes very large, ln(B/A) grows without bound and the capacitance tends toward zero. So the qualitative effect is that the capacitance decreases as the outer radius grows.

Capacitance in a coaxial cylinder depends on the logarithm of the radius ratio, through C = 2π ε0 L / ln(B/A). With the inner radius A fixed, increasing the outer radius B makes the ratio B/A larger, so ln(B/A) grows. Since the numerator (2π ε0 L) is fixed for a given length, a larger denominator means a smaller capacitance. In the extreme where B becomes very large, ln(B/A) grows without bound and the capacitance tends toward zero. So the qualitative effect is that the capacitance decreases as the outer radius grows.