You would like to store 8.2 J of energy in the magnetic field of a solenoid. The

Question

You would like to store 8.2 J of energy in the magnetic field of a solenoid. The solenoid has 550 circular turns of diameter 8.2cm distributed uniformly along its 23cm length. Part A How much current is needed? Express your answer using two significant figures. I= 43 A Part B What is the magnitude of the magnetic field inside the solenoid? Express your answer using two significant figures. B= 0.13 T Part C What is the energy density (energy/Volume) inside the solenoid? Express your answer using two significant figures. uB= kJ/m^3

Explanation / Answer

the energy stored in the inductor is

E = 1/2 L i^2

i = root 2 U/L

= root 2 U I/oN2 A

= root 2 (8.2 J)( 0.23 m)/ 4 pi * 10 ^-7 ( 550) ^2 ( pi ( 0.041 m)^2

=43.36 A

(b)

the magnetic field inside solenoid is

B = uo n i

= 4 pi * 10 ^-7 ( 550/0.23 m)( 43.36 A)

=0.13 T

(c)

UB = B2 / 2o= ( 0.13 )^2/ 2 ( 4 pi * 10 ^-7)

=6.72 kJ/ m^3

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.