A 20 cm-long solenoid is constructed of 1500 turns of wire wrapped around a 2 cm
ID: 1454875 • Letter: A
Question
A 20 cm-long solenoid is constructed of 1500 turns of wire wrapped around a 2 cm diameter core in the direction shown in the figure. A pickup coil composed of 190 turns of wire is wrapped tightly around the core at the middle of the solenoid in the opposite direction. The resistance of the pickup coil is 3?. The current through the solenoid is initially 0 and then increases to 16 A in 2 seconds.
1)When the current is 16 A (see figure for the direction), what is the magnitude of the magnetic field in the solenoid?
2)When the current is 16 A (see figure for the direction), what is the direction of the magnetic field in the solenoid?
3)When the current is 12 A in the solenoid, what is the magnetic flux, ?B, through one turn of the pickup coil?
4)During the 2 seconds when the current in the solenoid is increasing what is the EMF (Volts) induced in the 190 turn pickup coil?
5)What is the direction of the induced current through the resistor?
6)What is the magnitude of the induced current through the resistor?
Please explain and show all your work! Thank you.
Explanation / Answer
1) magnetic field in solennoid = ( 4 * 3.14 * 10-7 * (1500/0.2) * 16)
= 0.1507 T
2) direction of magnetic field = towards left .
3) magnetic flux = ( 4 * 3.14 * 10-7 * (1500/0.2) * 12) * 3.14 * 0.01 * 0.01
= 3.549 * 10-5 Wb
4) magnetic field in solennoid = ( 4 * 3.14 * 10-7 * (1500/0.2) * I)
= 9.42 * 10-3 * I
=> magnetic flux = 9.42 * 10-3 * I * 3.14 * 0.01 * 0.01 * 190
= 5.62 * 10-4 * I
=> induced emf = 5.62 * 10-4 * 16/2
= 4.496 * 10-3 V
5) direction of the induced current through the resistor = towards right .
6) induced current = 4.496 * 10-3 /3
= 1.5 * 10-3 A
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