Mutual Inductance (ouch, my brain)

[Dart82]

Homework Statement

During a 65 ms interval, a change in the current in a primary coil occurs. This change leads to the appearance of a 6.0 mA current in a nearby secondary coil. The secondary coil is part of a circuit in which the resistance is 12 . The mutual inductance between the two coils is 3.1 mH. What is the magnitude of the change in the primary current?

Homework Equations

mutual inductance: M = (number of loops in coil 2 * flux through coil 2)/ current of coil 1

Faradays law
emf = -M x (change in voltage of coil 1/change in time)

The Attempt at a Solution

i could use faraday's law to solve for change in current of coil 1, but i don't know what the emf is.
i know the formula for emf is vBL, but i don't know v, B, or L!
i can't use the mutual inductance formula because i don't know the # of loops in coil 2.
If someone could please point me in the right direction here i would greatly appreciate it.

 

[anathema]

I would start by gathering all the information given in the problem and identifying what is known and what is unknown. From the problem, it is known that there is a change in current in the primary coil, which results in a 6.0 mA current in the secondary coil. The resistance and mutual inductance between the two coils are also given. This means that we have values for the current in the secondary coil, resistance, and mutual inductance, but we need to find the change in current in the primary coil.

Next, I would review the equations and formulas that relate to mutual inductance, Faraday's law, and the emf. From Faraday's law, we know that the emf is equal to the negative of the mutual inductance multiplied by the change in current over time. This means that we can rearrange the equation to solve for the change in current of the primary coil, which is what we are looking for.

We also know that the emf is equal to the product of the magnetic field (B), the length of the coil (L), and the velocity of the coil (v). However, we do not have values for B, L, or v. This is where our knowledge of the problem and basic principles of electromagnetic induction come into play.

We know that the change in current in the primary coil results in a change in the magnetic field, which then induces a current in the secondary coil. We also know that the mutual inductance is a measure of the coupling between the two coils, which is affected by factors such as the number of turns in the coils and their relative positions.

Therefore, we can use this information to determine the change in magnetic field and the velocity of the coil, and then use this to solve for the change in current in the primary coil. Additionally, we can use the given resistance and current in the secondary coil to calculate the voltage (V = IR) and then use this value to solve for the velocity (v = V/BL).

Once we have determined the velocity and change in magnetic field, we can plug these values into the equation for the emf to solve for the change in current in the primary coil.

In summary, as a scientist, I would approach this problem by gathering all the information given, reviewing relevant equations and principles, and then using this information to determine the unknown values and solve for the change in current in the primary coil.

 

[m2003]

I understand that the concept of mutual inductance can be complex and difficult to grasp. However, it is a fundamental principle in electromagnetism and plays a crucial role in many real-world applications. Let's break down the problem and see if we can make sense of it together.

First, let's review the definitions of mutual inductance and Faraday's law. Mutual inductance is a measure of the ability of two coils to induce a voltage in each other. It depends on the number of turns in each coil, the magnetic flux through the coils, and the current in one of the coils. Faraday's law states that the induced emf (electromotive force) in a coil is equal to the rate of change of magnetic flux through the coil.

Now, let's apply these concepts to the problem at hand. We know that a change in the current in the primary coil leads to a current in the secondary coil. This implies that there is a changing magnetic flux through the secondary coil, which in turn induces an emf in the secondary coil. We also know the resistance and mutual inductance of the secondary coil. So, we can use Faraday's law to calculate the induced emf in the secondary coil.

Next, we can use Ohm's law (V=IR) to calculate the voltage across the secondary coil. We know the resistance and current in the secondary coil, so we can solve for the voltage. This voltage is equal to the induced emf from Faraday's law.

Now, we can use the mutual inductance formula to calculate the change in current in the primary coil. We know the mutual inductance, the number of turns in the secondary coil (which is the same as the primary coil), and the induced emf from the previous step. We can rearrange the formula to solve for the change in current in the primary coil.

I hope this helps guide you in the right direction. It may seem daunting at first, but with careful application of the relevant equations and concepts, you can solve this problem and deepen your understanding of mutual inductance. Keep up the good work!