One solenoid is centered inside another. The outer one has a length of 3.0 cm, a
ID: 1518739 • Letter: O
Question
One solenoid is centered inside another. The outer one has a length of 3.0 cm, a radius of 16.5 cm and contains 310 turns. The coaxial inner solenoid is 4.0 cm long and 6.5 cm in radius and contains 4850 turns. The current in the outer solenoid is moving into the page at the top so it wraps away from you as it moves upwards through the outer coil. That 2nd coil’s current in icnreasing at a rate of +42.5 A/s. (a) What is the mutual inductance of these solenoids? (b) Find the emf induced in the inner solenoid. (c) What direction is the current that is induced in the inner soilenoid if viewed from the right, looking left (clockwise or counter clockwise)?
3m-1 16.5 cm 4- 6.5 cm CIn Inside solenoid has 4850 turns Outside solenoid has 310 turnsExplanation / Answer
(a) The mutual inductance of two solenoids is given by M = µo*A*N1*N2/L, where A and L are the cross-sectional area inside the solenoids and length of the outer solenoid, respectively.
M = (4pi*10^-7*pi*0.065^2*310*4850)/0.03 = 0.836 H
(b) To compute Einner, we use Einner = M(dI/dt) = 0.836*42.5 = 35.53 V
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