Electric Field Direction for Electron Moving Parallel to Wire

[pat666]

Homework Statement

4 A long, straight wire carries a current of 25.0 A. An electron is fired parallel to this wire with a velocity of 250 km.s-1 in the same direction as the current, 2.00 cm from the wire.
a) Find the magnitude and direction of the electron’s initial acceleration.
b) What should the magnitude and direction of a uniform electric field be that will allow the electron to continue to travel parallel to the wire?

Homework Equations

The Attempt at a Solution

B=kI/d
B=2.5*10^-4 T
F=Bqv
F=1*10^-17N
F=ma
a=1.099*10¹²m/s²

E=F/q
E=62.5N/c
I'm relatively confident with my numerical answers although I would appreciate someone looking over my basic procedure. I run into trouble tying to explain the direction of the field.
Were using conventional current (don't ask me why) and the best indication of the direction I can give is "at 90⁰ away from the wire", thoughts?
Thanks.

 

[ehild]

Check if you used proper value for the electron mass.

As for direction of electric current: By definition, the electric current flows in the direction of motion of the positive particles. When an electron is concerned, we speak about its velocity and the current it carries flows in the direction opposite to the velocity.

When you calculate the Lorentz force, it is $$\vec {F}=q \vec{v}\times \vec{b}$$. You can clearly see the direction of F from the vector product, but there is a right-hand rule also for this. If v and B are perpendicular as is the case here, imagine a coordinate system with x-axis pointing in the direction of v, the y-axis pointing in the direction of B. The force points in the positive z direction if it is a positive charge. You have an electron , so the force will point in the negative z direction. Check if it is away or towards the wire. The electric force should be opposite, but the electric field is opposite again to the force as the charge of electron is negative.

ehild

 

[pat666]

Thanks ehild, yeah I did use the wrong value for mass, now I get a=6*〖10〗^9 m/s^2...
Regarding the direction should it be "90degrees towards the wire"? I always seem to get the exact opposite direction on these problems for some reason?
really appreciate you picking up on my stupid little mistakes- I would never have found that when checking.

 

[ehild]

Thanks ehild, yeah I did use the wrong value for mass, now I get a=6*〖10〗^9 m/s^2...

It is even worse. The mass of electron is 9.1*10^-31 kg.
Regarding the direction should it be "90degrees towards the wire"? I always seem to get the exact opposite direction on these problems for some reason?

I think, yes, but who knows if there are so many opposite directions?

You seem to have the custom to contradict

ehild

 

[pat666]

Just realized when you said to check my mass I went ahead and googled mass of proton for some reason--brain explosion!

 

[Terocamo]

Thanks ehild, yeah I did use the wrong value for mass, now I get a=6*〖10〗^9 m/s^2...
Regarding the direction should it be "90degrees towards the wire"? I always seem to get the exact opposite direction on these problems for some reason?
really appreciate you picking up on my stupid little mistakes- I would never have found that when checking.

I think you shoulb be using Fleming's left hand rule to find the direction of the electron,
it should be away from the wire. Or you can try to find out the vector multipler of IxB by certain
right hand ehilid mentioned. (two are different)

 

[ehild]

Just realized when you said to check my mass I went ahead and googled mass of proton for some reason--brain explosion!

Never mind...

ehild

 

[pat666]

I think you shoulb be using Fleming's left hand rule to find the direction of the electron,
it should be away from the wire. Or you can try to find out the vector multipler of IxB by certain
right hand ehilid mentioned. (two are different)

I got away from wire by using Flemings LHR to but I am terrible at finding directions for problems like this. so is it toward or away from the wire?

 

[Terocamo]

I got away from wire by using Flemings LHR to but I am terrible at finding directions for problems like this. so is it toward or away from the wire?

I'd say LHR is easier to use but $$\vec{I}$$ x $$\vec{B}$$ (by fanning your palm from I to B, your tumb is the direction of force) is faster.
It is away from the wire if you are taking about direction of electron movement.

 

[ehild]

I tried to make a drawing to show the magnetic force on that electron. But the direction of the force can also be obtained if you think of two parallel current-carrying wires: If the current flows in the same direction in the wires, they attract each other. In case of opposite direction of currents, the wires repel each other.
The electrion moves in the same direction as the current flows in the wire, but it is a negative charge, so it represents an opposite current.
Think it over to be sure of your answer about the direction of the electric field.


ehild