Hall effect/force on current carrying wire

[Tanishq Nandan]

Homework Statement

A metal strip 8.5cm long,0.65 cm wide,0.76 mm thick moves with constant velocity v through a uniform magnetic field B=0.2mT directed perpendicular to the strip,as shown in figure.A potential difference of 3.9 microV is measured between points x and y across the strip.Calculate the speed v.

Homework Equations

●E=V/d,
where d is width of strip,V is potential difference(Hall potential) across that width(3.9microV,here) and E is the electric field inside that strip.
●n=Bi/Vet,
where
n=no of conduction electrons per unit volume of strip
B=magnitude of magnetic field
i=current flowing through that strip
V=Hall potential,described in previous formula
e=charge on electron
t=thickness of strip(0.76 mm here)
●Basic theory of Hall effect:On applying a magnetic field perpendicular to the strip,some electrons get accumulated at one side of the strip due to the magnetic force acting on them,which after a while causes an electric field to be produced inside the strip across it's width,which opposes and finally cancels the effect of the magnetic field,thus allowing current(which is nothing but charged particles) to flow through the strip unhindered.

The Attempt at a Solution

I don't understand how the entire strip is moving.
Hall effect is about the two fields (electric and magnetic) cancelling out each other.but how can the entire strip move with a constant velocity.
Things i feel we may need to do:
Find n (2nd formula above) to get total no of conduction electrons,and find total force due to each of them due to the magnetic as well as electric field,but then there are several problems,
1.we don't know current (i in the formula)
2.what to do with the electrons which are accumulated on eithe side on the strip,responsible for the electric field being created,is the force on them just magnetic or electric as well??
So, I am not able to grasp what exactly happens to make the entire strip move.
(there is also the formula of F=BIL but I didn't mention it because again,we don't know current)

 

[TSny]

The situation in this problem is not the same as the situation for the Hall effect. In this problem, there is no electric current being driven along the length of the strip and the strip is moving through the B field. In the Hall effect, you have the opposite: there is an electric current and the strip is not moving through the B field.

You do not need to be familiar with the Hall effect to answer this question.

The strip is a metal. Think about what the magnetic field does to the free charge carriers in the metal.

 

[Tanishq Nandan]

You do not need to be familiar with the Hall effect to answer this question.

Okk..

Think about what the magnetic field does to the free charge carriers in the metal.

The B field exerts a force on the electrons causing them to move towards the "y" side of the strip,which I believe is the reason for the difference in potential between x and y,but then how does all this make the entire strip move FORWARD??

 

[TSny]

The motion of the strip is not due to the magnetic field. The question wants you to assume that the strip is moving with constant velocity. The motion of the strip could be due to some external agent (although once the strip is moving with constant speed, a force would not be required to keep it moving). So, don't worry about why the strip is moving.

 

[TSny]

The B field exerts a force on the electrons causing them to move towards the "y" side of the strip,which I believe is the reason for the difference in potential between x and y

Yes.

 

[Tanishq Nandan]

Well,then if I can't use any of the formulae I mentioned above,or Hall effect,which one should I use to find the velocity?
F=BIL??
But,we still need the current for that..

 

[TSny]

When the strip first starts moving with speed v, electrons move toward the right side and a potential difference develops between the left and right sides. Does this potential difference continue to increase as long as the strip is moving at constant speed, or does the potential difference attain a constant value?

What prevents the potential difference from continually increasing?

 

[Tanishq Nandan]

It attains a constant value(enough to create an electric field which cancels the magnetic field).

 

[Tanishq Nandan]

It attains a constant value(enough to create an electric field which cancels the magnetic field).

 

[TSny]

The electric field doesn't cancel the magnetic field. But the electric force cancels the magnetic force. Use this to determine the electric field.

 

[Tanishq Nandan]

Of course!
E=V/d
qE=Bqv
q gets cancelled..E can be determined,B is known,you got v.
Thanks..

 

[TSny]

Yes, very good.