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Question: A short solenoid of radius *a,* number of turns per unit length *n*}, and length *L* is kept coaxial...

A short solenoid of radius a, number of turns per unit length n}, and length L is kept coaxially inside a very long solenoid of radius b, number of turns per unit length n2. What is the mutual inductance of the system?

A

μ0πb2n1n2 L\mu _ { 0 } \pi b ^ { 2 } \mathrm { n } _ { 1 } \mathrm { n } _ { 2 } \mathrm {~L}

B

μ0πa2n1n2 L2\mu _ { 0 } \pi \mathrm { a } ^ { 2 } \mathrm { n } _ { 1 } \mathrm { n } _ { 2 } \mathrm {~L} ^ { 2 }

C

μ0πa2n1n2 L\mu _ { 0 } \pi \mathrm { a } ^ { 2 } \mathrm { n } _ { 1 } \mathrm { n } _ { 2 } \mathrm {~L}

D

Answer

μ0πa2n1n2 L\mu _ { 0 } \pi \mathrm { a } ^ { 2 } \mathrm { n } _ { 1 } \mathrm { n } _ { 2 } \mathrm {~L}

Explanation

Solution

The mutual inductance of the system is

M=μ0πa2n1n2 L\mathrm { M } = \mu _ { 0 } \pi \mathrm { a } ^ { 2 } \mathrm { n } _ { 1 } \mathrm { n } _ { 2 } \mathrm {~L}