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

Magnetic Field Induced Current

  • #1

Homework Statement


A uniform magnetic field
Barrowitalic.gif
is perpendicular to the plane of a circular loop of diameter 18 cm formed from wire of diameter5.0 mm and resistivity 1.69 ✕ 10−8 Ω · m. At what rate must the magnitude of
Barrowitalic.gif
change to induce a 10 A current in the loop

Homework Equations


Φ = ∫ B ⋅ dA (in vector form)
φ= BA
ε= -dΦ/dt
ε=IR
R= ρL/A

The Attempt at a Solution


Current is given, so I fould the Emf using ε=IR
ε= (10) x ((1.69E-8)(2π⋅0.09))/(π⋅0.0052)) = 0.001217

Then using the value obtained for ε,
0.001217 = dΦ/dt
Φ= BA

0.001217⋅A = dB/dt

wouldn't dB/dT be the rate that B is changing?
 

Answers and Replies

  • #2
34,038
9,880
wouldn't dB/dT be the rate that B is changing?
It is, but the units are not Ampere. In general, working with units helps to find most errors.
Be careful with diameter and radius of the wire.
 
  • #3
Oh I see, my mistake was actually I used diameter instead of radius. Thank you!
 

Related Threads for: Magnetic Field Induced Current

  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
2
Views
5K
Replies
12
Views
675
Replies
3
Views
4K
Replies
3
Views
450
Replies
2
Views
627
Top