Physics homework questions

Question

1) Suppose that when you move a magnet through a 26.3-turn coil at a certain speed, a voltage of 51.0 Volt is induced across the coil. If you move the same magnet through a 445.5-turn coil at the same speed, what voltage will be induced across the coil, assuming both coils are closely packed? The answer is
Volt.

2) If 32.4 volt power supply is connected to a lamp with resistance 1.2 ohm. What would be the magnetic field induced at a point 4.4 centimeter away from the lamp? The answer is
Tesla. 

3) If a 0.6T bar magnet is pushed through a 57.7 turn coli with an area of 0.003m2 in 2.9sec. The induced magnetic field is ___T. 

4) If 7.586 A current is passing through a straight wire, what would be the magnetic field induced at a point 3.9 centimeter away from the wire? The answer is
Tesla. 

Answer 1

I think I can set up a solution to (3), but I agree with Steven that more information is needed, at least for the approach that I am suggesting.

 

If you have a current i through a solenoid, it produces a magnetic field

 

B = μ₀ni

 

n = (number of turns) / (length of solenoid) = N/L

 

The B above is what we want.  So as Steven pointed out, we need to find a way to get that current i flowing through the solenoid.

 

If we knew the resistance of the solenoid, we could divide the induced emf by the resistance to get the induced current i.  We still need the induced emf E, which we can get from Faraday's law:

 

E = -dΦ/dt

 

Φ = magnetic flux = BA 

 

E = -(dB/dt)A = -(ΔB/Δt)A   (A= constant = 0.003 m²)

 

ΔB = B_f - B_i = 0.6T - 0

 

Δt = 2.9 s

 

We now have sufficient information to find E.  Then i = E/R, where R is the resistance of the solenoid, which we do not have.  But if we found i, we could plug it into

 

B = μ₀ni

 

But we need to also know the length L of the solenoid.  We are given N = 57.7, but we need N/L = n.

 

[Steven, does this approach make sense to you?]

 

Answer 2

Hi Juan!

 

1)  Faraday's law, which governs this kind of electromagnetic induction, depends directly on the number of turns in the coil (assuming close packing of the coils).  So, all else being equal, the induced voltage increases in direct proportion with the number of coils.  So we can say:

 

51 Volts  =   n Volts

----------      --------

26.3 turns     445.5 turns

 

and solve for the new induced emf (voltage)

 

2)  I think that what they are going for here is the magnetic field a certain distance from the (supposedly) single wire that is supplying the electricity to the lamp.  If we model this as a long, straight wire, then the magnetic field a certain radial distance away is given by:

 

B = μ_oi/(2πr)

 

What you have to do with the given information is determine the current running in the wire.  That you can get from V = iR, with the voltage of the power supply V and the resistance R of the bulb given.

 

4) Is done the same way as 2), using that expression for the magnetic field from a long straight wire.  Just make sure to convert your length units to meters.

 

3) is a little trickier.  To get the magnetic field, rather than the induced emf, we have to know something about the magnitude of the induced current, because we have to go from induced emf (voltage) to current through V = iR (as in some of the other problems).  Without that information, I am not sure how to calculate the induced field's magnitude.  Is there any other information for this problem?  I will also think about it more and see if anything else occurs to me.

 

Hope this helps some!  Let me know if you have more information or other questions.