Consider a system consisting of two long, concentric solenoids, as shown below i
ID: 1482974 • Letter: C
Question
Consider a system consisting of two long, concentric solenoids, as shown below in cross section. The current in the outer solenoid is I1 = 1.80 A, while the current in the inner solenoid is I2 = 3.41 A flowing in the opposite direction. The outer solenoid has 103 turns per centimeter, and the inner solenoid has 123 turns per centimeter.
Find the magnetic field strength in the region between the two solenoids. Enter your answer as a positive number if the field points up.
Find the magnetic field strength inside the inner solenoid. Enter your answer as a positive number if the field points up.
Explanation / Answer
Given that
The current in the outer solenoid is I1 = 1.80 A,
while the current in the inner solenoid is I2 = 3.41 A flowing in the opposite direction.
The outer solenoid has 103 turns per centimeter, and the inner solenoid has 123 turns per centimeter.
The magnetic field inside a outer solenoid is
Bout =uonI1
=uo(N/L)I1 =(4*3.14*10-7)(103*102)(1.80)=0.02328T and this will be in the upward direction
Now the magnetic field inside a inner solenoid is
Bin =uonI2
=uo(N/L)I2 =(4*3.14*10-7)(123*102)(3.41)=0.05268T and this will be in the downward direction
Therefore the magnetic field between the two solenoids is equal to the magnetic fielddue to outer solenoid
Bout =0.02328T =23.28mT direction will be in upwards
b)
If the magnetic field strength inside the inner solenoid is given by
B =Bout-Bin
=0.02328T-0.05268T
=-0.0294T or -29.4mT