Understanding the Relationship Between Time and Magnetic Field Induction

In summary, the conversation discusses the relationship between a changing magnetic field and an induced emf in a wire loop. It is determined that the magnitude of the magnetic field must be proportional to t^2 in order for the induced emf to increase linearly with time t. The conversation also touches on the notation of emf(kt) and the steps to get from emf = d(BA)/dt to emf(kt) = BA.
  • #1
appliedF
16
0

Homework Statement


A magnetic field perpendicular to the plane of a wire loop is uniform in space but changes with time tin the region of the loop. If the induced emf in the loop increases linearly with time t, then the magnitude of the magnetic field must be proportional to:
a)t^3
b)t^2 <answer
c)t
d)t^0
e)t^1/2

Can someone explain this

I did emf=dflux/dt
emf(kt)=BA
B is proportional to t right?
 
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  • #2
I did emf=dflux/dt
emf(kt)=BA
I’m not understanding the notation on the left side of the second equation. What does emf(kt) mean?
 
  • #3
TSny said:
I’m not understanding the notation on the left side of the second equation. What does emf(kt) mean?
kt to show t is linear
 
  • #4
appliedF said:
kt to show t is linear
I'm still not understanding the notation emf(kt). Does it denote emf multiplied by kt? Or, is it saying that the emf is the same thing as kt? Or something else?

Going back to the previous equation, you have correctly stated that

emf = d(flux)/dt.

Express emf in terms of t on the left and express flux in terms of B and A on the right. After doing this, integrate both sides with respect to time.
 
  • #5
TSny said:
I'm still not understanding the notation emf(kt). Does it denote emf multiplied by kt? Or, is it saying that the emf is the same thing as kt? Or something else?

Going back to the previous equation, you have correctly stated that

emf = d(flux)/dt.

Express emf in terms of t on the left and express flux in terms of B and A on the right. After doing this, integrate both sides with respect to time.
d(flux)/dt=AdB/dt
dt's would cancel out leaving d(flux)=AdB
flux/A=B
What am I missing here?
 
  • #6
appliedF said:
d(flux)/dt=AdB/dt
dt's would cancel out leaving d(flux)=AdB
flux/A=B
What am I missing here?
There is nothing wrong here. I think the problem is how you are handling the left side of the equation emf = d(BA)/dt.

Can you explain in words the steps you took in getting from emf = d(BA)/dt to emf(kt) = BA? (I still don't understand the meaning of "emf(kt)".)

You went from emf = d(BA)/dt to emf(kt) = BA.

What operation did you perform on the right-hand side to get from d(BA)/dt to BA? Did you apply this same operation to the left side?
 
  • #7
TSny said:
There is nothing wrong here. I think the problem is how you are handling the left side of the equation emf = d(BA)/dt.

Can you explain in words the steps you took in getting from emf = d(BA)/dt to emf(kt) = BA? (I still don't understand the meaning of "emf(kt)".)

You went from emf = d(BA)/dt to emf(kt) = BA.

What operation did you perform on the right-hand side to get from d(BA)/dt to BA? Did you apply this same operation to the left side?
t is linearly related to the emf, so i incorrectly changed dt to kt and multiplied it to emf and took out the derivative for BA.

But the dt's cancel out right? how do you get t^2
 
  • #8
appliedF said:
t is linearly related to the emf
Yes, so emf = kt where k is a constant.

So, starting with emf = d(BA)/dt you can write

kt = d(BA)/dt.

Can you proceed from here?
 
  • #9
TSny said:
Yes, so emf = kt where k is a constant.

So, starting with emf = d(BA)/dt you can write

kt = d(BA)/dt.

Can you proceed from here?
yes thanks bud
 

1. What is a magnetic field?

A magnetic field is a region in space where a magnetic force can be detected. It is created by moving electric charges, such as electric currents, and is characterized by its direction and strength.

2. How is a magnetic field measured?

A magnetic field can be measured using a device called a magnetometer. This device detects the strength and direction of the magnetic field and provides quantitative measurements.

3. What is magnetic induction?

Magnetic induction, also known as electromagnetic induction, is the process of creating an electric current in a conductor by exposing it to a changing magnetic field. This phenomenon is the basis for many electrical devices, such as generators and transformers.

4. What factors affect the strength of a magnetic field?

The strength of a magnetic field is affected by the magnitude of the electric current or magnetic material creating it, the distance from the source, and the geometry of the magnetic field. In addition, the presence of other magnetic fields can also influence its strength.

5. How is a magnetic field used in everyday life?

Magnetic fields have a wide range of applications in everyday life, such as in electric motors, generators, speakers, and magnetic storage devices like hard drives. They are also used in medical imaging techniques like MRI and in compasses for navigation.

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