What Rate of Magnetic Field Change Induces a 10 A Current in a Circular Loop?

[PhysicsInNJ]

Homework Statement

A uniform magnetic field

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

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?

 

[mfb]

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.

 

[PhysicsInNJ]

Oh I see, my mistake was actually I used diameter instead of radius. Thank you!