How Fast Must a Magnetic Field Change to Induce a Specific Current?

AI Thread Summary
To induce a current of 0.22 A in a conducting loop with an area of 7.4 x 10^-2 m^2 and a resistance of 110 ohms, the rate of change of the magnetic field must be calculated. The magnetic flux is given by the formula Φ = BA, and the induced electromotive force (EMF) is related to the change in flux over time, expressed as E = dΦ/dt. Using Ohm's law, the relationship E = IR can be applied to find the necessary induced EMF for the desired current. By rearranging these equations, the required rate of change of the magnetic field in teslas per second can be determined. Understanding these relationships is crucial for solving the problem accurately.
triplezero24
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Ok, I need a lot of help on this one. A single conducting loop of wire has an area of 7.4*10^-2 m^2 and a resistance of 110 ohms. Perpendicular to the plane of the loop is a magnetic field of strength 0.18 T. At what rate (in T/s) must this field change if the induced current in the loop is to be 0.22 A?

So far all I can figure out is that Phi=BA. And I don't think that has anything to do with this problem.

Thanks for any and all help.
 
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Well, how do you relate the change in flux to the induced EMF? And once you have that, just use ohm's law to get the current.
 
you should know these formulae from your text

flux \Phi = \int B dA Cos \theta
and induced emf E = \frac{d \Phi}{dt}
and also the induced Emf is just live a voltage really so E = IR.

now try and rearrange these equatios to solve
 
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