Solving for the Changing Magnetic Field in a Conducting Loop

[Lance WIlliam]

A conducting loop of area 240cm^2 and resistance 14(Ohm symbol) lies at right angles to a spatially uniform magnetic field. The loop carries an induced current of 320mA .



At what rate is the magnetic field changing?

dB/dt= T/s

Ok...
So, I use Faraday's Law

Which is That "E" Symbol..=d(magnetic Flux)_B_/dt

Im given resistance so I am assuming I can use the formula I=E/R ...I have R(14) and the induced current which is 320mA...
So I can find "E"...
But what do I do from there...Im pretty lost on this stuff...@_@
Thankyou.

 

[Gear300]

Rather than calling it an "E" symbol, its better if you call if emf (which is voltage...I'm sure you know this, its just that using E might get things confused with electric field). Faraday's law shows that a changing magnetic flux/field induces a voltage. So in this case, the changing magnetic field is inducing a voltage across the conducting loop. V = -d(PhiB)/dt, in which PhiB is magnetic flux. I = V/R, thus V = IR. With this you have the voltage. Magnetic flux is BAcos(theta). You have the angle and area and it doesn't seem that the problem says these 2 values are changing, so you can take them to be constant. So from this, you can evaluate dB/dt.

 

[Lance WIlliam]

Ok so...Ur using "V" as emf. Got it.
dB/dt...the derivative...of..Where do I get "B" to even solve for mag. flux?
I See V=(14)(320mA) so I have
V=-d(phiB) which is BAcos(theta) But how do I get "B"?
and once found what is my dt?

 

[Gear300]

d(phiB)/dt refers to derivative of magnetic flux in respect to time...if you're unfamiliar with calculus, then don't worry...in this case you could look at it as Delta(phiB)/Delta(t), which is equal to Delta(B*A*cos(theta))/Delta(t). Since A and cos(theta) are constant, you could pull those out so that it becomes A*cos(theta)*Delta(B)/Delta(t)...Delta(B)/Delta(t) refers to change in magnetic field over time, which is what you're looking for.

 

[Lance WIlliam]

And I can solve for B by using I=E/R Since I have "R and "I" and I know E is B(pi)r^2 and I know what "r" (since I know area)is I can solve for "B" using [B(pi)r^2)=IR Then I'll have "B" So I pull out my constants on the intergral so its A*cos (Delta B/Deltat)
But How do I go about finding "t"?