Problems about magnetic field, electromotive force, induced current

[Dominic90]

Homework Statement

- The pick up (magnet with coil wound around) of an electric guitar is such that in coil, formed by 10 circular turns with a radius of 4 cm and whose surfaces are perpendicular to the lines of force of the magnetic field, an induced current of 2 x 10^(-4) A arises when the field average magnetic on the surface of the coil passes from an unknown value B1 to a value of 2.3 T in 0.05 s. Determine the initial magnetic field knowing that the coil has a resistance of 2000 Ω and neglecting Lenz's law.



- Consider an area of 3.96m^2; it is immersed in a uniform magnetic field B0 = 0.9 T crossed perpendicularly by the lines of B. At a certain instant the intensity of the field begins to vary over time according to the law:

𝐵 (𝑡) = 𝐵0 (0.4𝑡^2 - 𝑙𝑛𝑡). To determine:

▪ the instant in which the electromotive force is zero.

▪ The absolute value of the electromotive force induced in the loop at the instant t = 5 s and of the induced current knowing that the loop resistance is 10 Ω.

Relevant Equations

Faraday's Law

Hi, I was practicing some problems on the magnetic field and the electromotive force, when I got stuck on these two exercises. Could you help me figure out how to proceed?

In the first problem, I tried to find the magnetic field flux by multiplying the induced current for ∆t and R. Should I now divide this result by the number N of turns?

In the second exercise, I started setting the flux equal to 0, then I'm at an impasse

 

[Delta2]

For the first problem your first task will be to find the voltage induced to the coil with two ways:

1. According to Faraday's Law
2. According to Ohm's law

Then equate the two and you ll be able to find what the problem asks for cause if all go well you ll have one equation with one unknown=the initial value of magnetic field.

For the second problem again you have to find the voltage (or electromotive force) according to Faraday's law. You know $B(t)$ and the area so you will be able to calculate the EMF $$\mathcal{E}(t)=-\frac{d\Phi}{dt}=-3.96\frac{dB(t)}{dt}$$. Then

1. Set this expression to zero and you ll have one equation with one unknown the time instant t at which the EMF is zero
2. Set in this expression the time t=5sec and you ll be able to find the $\mathcal{E}(5)$ and by using Ohm's law the current at time t=5sec.