Calculating the energy stored in the magnetic field within the solenoid

문제)

An air-core solenoid with 68 turns is 8.00cm long and has a diameter of 1.20cm. When the solenoid carries a current of 0.770A, how much energy is stored in its magnetic field within the solenoid?

 

풀이)

magnetic field에 stored된 energy를 구하는 공식은 아래와 같다.

 

U = 1/2 × I^2 × L

L = μ0 × N^2 × A ÷ l

 

μ0 = 4π × 10^-7 Tm/A

N = 68

l = 8.00 × 10^-2 m

r = 1/2 × 1.20cm = 0.60cm = 6.00 × 10^-3 m

A = π × r^2 = 36.0 × 10^-6 × π cm^2

 

L = ( 4π × 10^-7 × 68 × 68 × 36.0 × 10^-6 × π ) ÷ 8.00 × 10^-2 = 8.21 × 10^-6 Tm^2/A

 

U = 1/2 × I^2 × L

I = 0.770A, L = 8.21 × 10^-6 Tm^2/A

U = 1/2 × 0.770A × 0.770A × 8.21 × 10^-6 Tm^2/A = 2.44 × 10^-6 J