Mutual Inductance of solenoid and coil

[hellogirl88]

Find the mutual inductance (H) of the solenoid and coil shown below. The solenoid has 5263 turns per meter and an area 112 cm^2, and the coil has 230 turns and an area 19 cm^2.


I know that mutual inductance = (N1 Φ1)/ I2 but I have no idea where to begin since they don't provide the current or flux. How can I find those?

Thanks!

 

[alphysicist]

Hi hellogirl88,

Find the mutual inductance (H) of the solenoid and coil shown below. The solenoid has 5263 turns per meter and an area 112 cm^2, and the coil has 230 turns and an area 19 cm^2.


I know that mutual inductance = (N1 Φ1)/ I2 but I have no idea where to begin since they don't provide the current or flux. How can I find those?

Thanks!

To use the mutual inductance formula, you assume that one of the objects (either the coil or the solenoid) has some current I, and then calculate the flux that is prodcued in the other object. (The answer will be the same no matter which one you use for the current, but the calculation is much easier for one than the other.)

(By the way, the diagram makes it look like the solenoid is short. I'm assuming that it is just supposed to show a small part of it, and the solenoid is really long.)

 

[nlightner]

To calculate the mutual inductance (H) of the solenoid and coil, we need to have information about the magnetic flux (Φ) and current (I). The magnetic flux is a measure of the amount of magnetic field passing through a given area, and it is directly proportional to the current. Therefore, we need to determine the current flowing through the solenoid and coil in order to calculate the mutual inductance.

One approach to finding the current is to use Ohm's Law (V=IR) where V is the voltage, I is the current, and R is the resistance. We can measure the voltage across the solenoid and coil using a voltmeter and then use the known resistance of the solenoid and coil to calculate the current.

Another approach is to use a current probe to directly measure the current flowing through the solenoid and coil. This method may be more accurate as it takes into account any variations in resistance.

Once we have determined the current, we can then calculate the magnetic flux using the formula Φ = B*A, where B is the magnetic field and A is the area. The magnetic field can be calculated using the formula B = μ0*N*I/L, where μ0 is the permeability of free space, N is the number of turns, I is the current, and L is the length of the solenoid.

Finally, we can plug the values for magnetic flux and current into the formula for mutual inductance (H) = (N1*Φ1)/I2 to find the mutual inductance of the solenoid and coil. It is important to note that the units for mutual inductance are henries (H).

In summary, in order to find the mutual inductance of the solenoid and coil, we need to determine the current flowing through them and the magnetic flux passing through them. This can be done by measuring the voltage and using Ohm's Law or using a current probe, and then calculating the magnetic field using the given formulas. Finally, we can plug these values into the formula for mutual inductance to find the desired result.