- #1
Sho Kano
- 372
- 3
Homework Statement
A uniform magnetic field is perpendicular to the plane of a circular loop of diameter 10 cm formed from wire of diameter 2.5 mm and resistivity 8.5×10-8 Ω·m. At what rate must the magnitude of the magnetic field change to induce a 10 A current in the loop?
Homework Equations
[itex]\phi \quad =\quad BA,\quad B\bot A\\ { V }_{ induced }\quad =\quad \frac { d\phi }{ dt } \quad =\quad IR\\ R\quad =\quad \frac { \rho { L }_{ 2 } }{ { A }_{ 2 } } [/itex]
The Attempt at a Solution
[itex]Givens:\\ \\ { d }_{ 1 }\quad =\quad 10/100\quad =\quad 0.1\quad meters\\ { r }_{ 1 }\quad =\quad \frac { { d }_{ 1 } }{ 2 } \quad =\quad 0.05\quad meters\\ { d }_{ 2 }\quad =\quad 2.5/1000\quad =\quad 0.0025\quad meters\\ { r }_{ 2 }\quad =\quad \frac { { d }_{ 2 } }{ 2 } \quad =\quad 0.0013\quad meters\\ { L }_{ 2 }\quad =\quad 2\pi { r }_{ 2 }\quad =\quad 0.0082\quad meters\\ { A }_{ 1 }\quad =\quad \pi { { r }_{ 1 } }^{ 2 }\quad =\quad 0.0079\quad sqr\quad meters\\ { A }_{ 2 }\quad =\quad { \pi { { r }_{ 2 } } }^{ 2 }\quad =\quad 5.31\quad x\quad { 10 }^{ -6 }\quad sqr\quad meters\\ I\quad =\quad 10A\\ \rho \quad =\quad 8.5\quad x\quad { 10 }^{ -8 }\quad \Omega \quad meters[/itex]
[itex]Calculations:\\ \frac { d\phi }{ dt } \quad =\quad { A }_{ 1 }\frac { dB }{ dt } \quad =\quad IR\quad =\quad I\frac { \rho { L }_{ 2 } }{ { A }_{ 2 } } \\ { A }_{ 1 }\frac { dB }{ dt } \quad =\quad I\frac { \rho { L }_{ 2 } }{ { A }_{ 2 } } \\ \frac { dB }{ dt } \quad =\quad I\frac { \rho { L }_{ 2 } }{ { A }_{ 2 }{ A }_{ 1 } } \quad =\quad 0.1665\quad T/s[/itex]
Which is wrong?