Total electrical resistance flux

[yitriana]

Homework Statement

The circular wire loop has 10 turns and a radius of 1.0 cm. The total electrical resistance of the 10 turn loop is 0.10 Ω. The magnitude of the magnetic field due to the solenoid near the wire loop at t = 0 s is 0.002 T. The current through the solenoid doubles between t = 2 s and t = 4 s.


What is magnitude of the rate-of change of the magnetic flux through the wire loop at t = 3 s?

Homework Equations

flux = NBA where N is number of turns of wire, B is magnetic field, A is area traversed by one loop

E = IR where E is induced emf on the wire

The Attempt at a Solution

I have calculated the flux accurately 6.28E-6 Wb, but I am having a lot of difficulty with the bolded question. I can't figure out how to manipulate the equations because I don't know the initial current, and I don't know the final magnetic field and I just can't simplify anything.

 

[kuruman]

How is the magnetic flux related to the current in the solenoid? By this I mean, is it directly proportional, inversely proportional, goes as the square of the current or what? If you can answer this question, then you can figure out by what factor the flux changes from t = 2 to t =3 s and then all you have to do is multiply the 6.28e-6 Wb by that factor to find the flux. Unless you have a figure that shows otherwise, you may assume that the current changes linearly with time.

 

[kerimek]

I understand your struggles with this problem. In order to calculate the rate of change of the magnetic flux through the wire loop at t = 3 s, we can use Faraday's Law, which states that the induced emf (E) in a closed loop is equal to the negative rate of change of the magnetic flux through that loop. In this case, the induced emf can be calculated using Ohm's Law (E = IR), where R is the total electrical resistance of the loop.

Since the current through the solenoid doubles between t = 2 s and t = 4 s, we can use the known resistance of the loop (0.10 Ω) to calculate the initial current at t = 2 s. Then, using the known increase in current, we can calculate the final current at t = 4 s.

Once we have the initial and final currents, we can use the equation B = μ0nI, where μ0 is the permeability of free space, n is the number of turns per unit length (in this case, n = 10 turns/length of the solenoid), and I is the current. This will give us the initial and final magnetic fields at t = 2 s and t = 4 s, respectively.

Now, using the known area of the loop (A = πr^2, where r is the radius of the loop), we can calculate the initial and final flux values at t = 2 s and t = 4 s. Finally, we can use the formula for average rate of change (Δflux/Δtime) to calculate the magnitude of the rate of change of the magnetic flux through the wire loop at t = 3 s.

I hope this helps you to solve the problem and better understand the concepts involved. Keep in mind that in science, it is important to approach problems systematically and use known equations and principles to solve them. Good luck!