• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Faraday's Law of Induction - Current in Multiple Wires

191
0
1. Homework Statement

A 7.40 cm diameter coil consists of 15 turns of circular copper wire 2.3 mm in diameter. A uniform magnetic field, perpendicular to the plane of the coil, changes at a rate of 7.29×10^−3 T/s . Determine the current in the loop. Express your answer using two significant figures.

2. Homework Equations

magnetic flux = BA
ε = -N Δmagnetic flux / ΔT

3. The Attempt at a Solution

I'm still a little confused as what to do with the 7.40 cm and 2.3 mm (other than convert them to SI units).

What I've done so far:

-15 (7.29 * 10^-3 T/s) = ε
ε = -0.109 V

Was that a good place to start?
 
6,049
390
The two radii are given so that you could determine the resistance of the wire in coil.
 
191
0
Would it make sense if I :

ε = - N (ΔB) / (Δt) * ∏r^2

This would provide a voltage.

R = ρl / a

This would provide a resistance.

I = V / R

This would provide a current.
 
6,049
390
The equation for EMF seems correct. In the equation for resistance, what are all those constants? How do they correspond to the data in the problem?
 
191
0
R is resistance.

ρ is the resistivity of the material (copper) = 1.72 * 10^-8 Ωm

l = length of wire = (0.0740 m?)

A = cross sectional area of wire = ∏(0.00115 m)

I'm unsure about the last two.
 
6,049
390
The values you listed for the last two are incorrect.

How would you compute the length of wire in a coil?

What about its cross-sectional area?
 
191
0
To calculate the length of a wire in a coil:

A coil is a circle. The circumference of a circle is ∏d. The coil has 15 turns so in this case

l = d∏ * 15

To calculate the cross sectional area of the copper wires:

A = ∏(0.00115 m)^2 * 15 (now I'm considering all of the turns).
 
6,049
390
The length looks good. But I don't understand why you multiply the cross-sectional area by the number of turns.
 
191
0
Wow! A = ∏r^2 . I just noticed in one of the comments I left off the "square" part.

A = ∏(0.00115 m)^2
 
6,049
390
So I think you have all it takes to solve the problem.
 

Related Threads for: Faraday's Law of Induction - Current in Multiple Wires

Replies
1
Views
6K
Replies
1
Views
5K
  • Posted
Replies
4
Views
2K
  • Posted
Replies
11
Views
3K
  • Posted
Replies
2
Views
3K
  • Posted
Replies
4
Views
787
Replies
5
Views
5K
Replies
2
Views
2K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top