Suppose you have a long, straight solenoid that has 760 turns of wire, a length
ID: 2260784 • Letter: S
Question
Suppose you have a long, straight solenoid that has 760 turns of wire, a length of 82 cm, and a circular cross-section of radius 4.4 cm.
a. Calculate the self-inductance of the solenoid, assuming that is is an "ideal" solenoid (l > r).
b. At a particular moment, suppose that a current of 25 A runs through a the solenoid. At that moment how much energy is contained in the solenoid's magnetic field?
c. If the current drops from 25 A to 12 A during 0.50 s, what is the average emf induced across the inductor?
Please show work for everything.
Explanation / Answer
a)
A=pir^2 =pi*(0.044)^2
A=6.08*10^-3 m^2
L=uoN^2A/l
L=(4pi*10^-7)*760^2*6.08*10^-3/0.82
L=5.383*10^-3 H or 5.383 mH
b)
B=uoNiL/l=(4pi*10^-7)(760)(25)/(0.82)
B=0.0291 T or 29.1 mT
c)
E =L(dI/dt) =5.383*10^-3*(25-12)/0.5)
E=0.14 V
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