A circular coil has a 10.0 cm radius and consists of 30.0 closely wound turns of wire. An exter

A circular coil has a 10.0 cm radius and consists of 30.0...

A circular coil has a $10.0 \mathrm{~cm}$ radius and consists of $30.0$ closely wound turns of wire. An externally produced magnetic field of magnitude $2.60 \mathrm{mT}$ is perpendicular to the coil. (a) If no current is in the coil, what is the magnitude of the magnetic flux that links its turns? (b) When the current in the coil is $3.80 \mathrm{~A}$ in a certain direction, the net flux through the coil is found to vanish. What is the inductance of the coil?

A circular coil has a $10.0 \mathrm{~cm}$ radius and consists of $30.0$ closely wound turns of wire. An externally produced magnetic field of magnitude $2.60 \mathrm{mT}$ is perpendicular to the coil.
(a) If no current is in the coil, what is the magnitude of the magnetic flux that links its turns? (b) When the current in the coil is $3.80 \mathrm{~A}$ in a certain direction, the net flux through the coil is found to vanish. What is the inductance of the coil?

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Self-Inductance

Self-inductance is the property of a coil that quantifies its ability to induce an electromotive force (emf) in itself as a result of a change in current. It is defined as the ratio of the magnetic flux linking the coil to the current flowing through it, and it plays a critical role in understanding energy storage in magnetic fields and the behavior of circuits with changing currents.

Magnetic Flux

Magnetic flux is a measure of the quantity of magnetism, taking into account the strength and the extent of a magnetic field. It is calculated by multiplying the magnetic field strength by the area through which the field lines pass, and it is a key concept in linking magnetic fields to the geometric properties of a surface.

Flux Linkage

Flux linkage extends the idea of magnetic flux to coils or multiple loops, being the product of the number of turns in the coil and the magnetic flux through one turn. This concept is essential when analyzing systems with various loops because it determines how effectively a magnetic field interacts with a coil to induce electromotive forces.

Transcript

00:01 Okay, so for this problem, we have a coil, and we're asked to find first the flux links through it, so we're given some information.

00:13 So the radius, there's 30 turns, and the radius is 0 .1 meters.

00:24 And then the magnetic field through the coil is 2 .6 times 10 to the minus 3 tesla.

00:34 And i want to find the flux link.

00:37 Excuse me, what was it called? this is kind of new vocabulary for me.

00:43 Magnetic flux links.

00:46 But i looked it up.

00:47 It's okay.

00:47 It's easy.

00:48 It's just phi is nba.

00:51 And then a is the cross -sectional area.

00:54 So nb.

00:55 P .r squared.

00:57 And then when i plug that into a calculator, i obtained 2 .45.

01:05 Times 10 to the minus 3 tesla meter squared.

01:12 And then the next part asks, oh, stop lagging.

01:18 I'm going to go slower, i guess.

01:21 The next part asks, when you turn on the current, and then the flux vanishes, what's the inductance of the coil? and so the, right, kind of inducing.

01:35 Not inducing, what about not inferring that the current through the coil creates a field, balances the external field.

01:49 And so, and we've first given that the i is 3 .8 amps...

Please give Ace some feedback