Mutual Inductance: Solving with Ampere's Law

AI Thread Summary
To solve for mutual inductance using Ampere's Law, one must calculate the magnetic flux through one circuit due to the current in another. The formula Φ = M*I indicates that mutual inductance is directly related to the magnetic flux. While Ampere's Law can be applied, it may require complex double integrals to account for contributions from each point along the wires. Alternatively, the Biot-Savart Law can be used to find the magnetic field at a point and then integrate over the area of the top loop to determine the flux. Understanding both methods is essential for effectively solving mutual inductance problems.
Frillth
Messages
77
Reaction score
0

Homework Statement



qq21ld.png


Homework Equations



Φ = M*I
Biot-Savart law
Ampere's law

The Attempt at a Solution



I have the formula Φ = M*I, which means that to find the mutual inductance I simply need to find the magnetic flux through the top circuit due to the current in the bottom circuit. However, I don't yet have a solid grasp of Ampere's law. Is there a way to use Ampere's law in this situation, or am I going to have to grind it out with Biot-Savart?
 
Physics news on Phys.org
Frillth said:
I have the formula Φ = M*I, which means that to find the mutual inductance I simply need to find the magnetic flux through the top circuit due to the current in the bottom circuit. However, I don't yet have a solid grasp of Ampere's law. Is there a way to use Ampere's law in this situation, or am I going to have to grind it out with Biot-Savart?

Looks like you will have a double integral for each point along the second wire for all the contribution from points on the first, then integrated over its own length.

See also:
http://en.wikipedia.org/wiki/Inductance#Mutual_inductance
 
Can I use Biot-Savart to find the magnetic field at some general point (x,y) in the plane, then integrate that over the area of the top loop to get flux?
 
What's the B-field of a long straight wire?
 

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

I Question about Capacitor current and electromagnetic induction
Replies
16
Views
1K
Inductance per unit length of coaxial transmission line
Replies
3
Views
14K
When do I use Biot-Savart Law vs. Ampere's Law?
Replies
2
Views
10K
Magnetic energy density, self-inductance of coaxial cylindrical shells
Replies
10
Views
1K
Finding magnetic field using Ampere's Circuital Law
Replies
5
Views
985
Magnetostatiscs: dipole moment and magnetic field
Replies
16
Views
2K
Mutual inductance coefficient with so little info
Replies
13
Views
2K
Calculating Self and Mutual Inductance: A Derivation of Formulas Using Solenoids
Replies
7
Views
2K
How to calculate the mutual inductance?
Replies
3
Views
2K
Question on magnetic fields from wire
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top