202301271158

27/01/23 11:59:10

@physics @electromagnetism @study @induction

Time: 1hr 30m

Need to start looking at practice questions.
Building up from Lenz’s law, to the magnitude of the induced current, to the power (by determining the force) as mentioned this force is part of the power generating thermal energy in the loop (right?).
Section 30-2 equating the work you do against the induced magnetic field to the thermal energy that ‘appears’ in the loop.

If we’ve a circular copper ring in a uniform magnetic field of radius R.
And we slowly increase the magnetic field strength, thus, changing the magnetic flux.
An emf is induced in the ring, the direction of that current (known by lenz law).
This creates an induced electric field (cause of this current).
This electric field appears even if there was no copper ring.
The electric field generated here, must be a set of concentric circles (as it induces a force such that current flows in a circular path).
A changing magnetic field produces an electric field

Induced electric fields are produced not by static charges but by a changing magnetic flux. Although electric fields produced in either way exert forces on charged particles, the difference is that the induced electric fields form closed loops.
Electric potential only has meaning then for fields created by static charge.
So if you have an induced emf of 5J/C. You would expect a charge under this influence to gain 5J of potential energy. But it can’t because it’s back in the same place in the field.
If the end point an start point were the same, in a conservative field like that of a static charge
$\oint E \cdot d s = 0$
But for a magnetic induced field this value is equal to $- \frac{d ϕ _{B}}{d t}$ .

Inductance is the tendency of a conductor to oppose a change in current flowing through it.
$L = \frac{N ϕ _{B}}{i}$
What are we quantifying here?
Storing energy in a magnetic field when current flows through it.
Need to think of inductor as storing energy (to be converted to motion of charge) in the magnetic field around a solenoid.
What does the magnetic field around a solenoid look like and in what direction does its field act?
- The force is always acting radially inwards [Induced electric field](#Induced electric field).
- The greater the current the more the magnetic field lines aggregate.
- It acts like a bar magnet that can be turned on and off. So just have that in my mind, will see if it’s a useful model.

When the current is constant the inductor is ‘happy’ it does not try to generate an opposing emf.
When the current stops, the inductor will generate a force, trying to keep the current flowing through it.

Book: Halliday