Calculating Electric Field: A Failed Attempt

[Zero]

Homework Statement

A proton, initially at rest is accelerated through a potential of 475 volts. The magnetic field (coming out of the plane of the page) has a magnitude of 1.5 Teslas. Determine the magnitude if the electric field strength such that the proton does not reflect and travels in a straight path.

Relevant Equations

Fel= Fm
qE= qvB
E= vB
E/B= v

v/Br= q/m
E/B^2r= q/m

I tried getting E by dividing volts and distance since I know the distance between the two plates is .352 m but it did not work

 

[haruspex]

It looks like part of the question is missing.
The 475V is what accelerates the proton in the first place, but I would say the electric field it asks about is between the plates (thick black lines) above and below the magnetic field.

 

[Zero]

It looks like part of the question is missing.
The 475V is what accelerates the proton in the first place, but I would say the electric field it asks about is between the plates (thick black lines) above and below the magnetic field.

Yes, you are correct but that is not the main issue here. The thing I have problems with is the many unknowns present in the question. If you look at the relevant formula then it would be easy to see that based on the question as far as I can see we don't have enough variables to start. My question to you is, based on the variables present in that formula what other variables or formula can we get from what we have? P.S that is exactly how the question is presented to me there are no missing parts.

 

[berkeman]

The thing I have problems with is the many unknowns present in the question. If you look at the relevant formula then it would be easy to see that based on the question as far as I can see we don't have enough variables to start. My question to you is, based on the variables present in that formula what other variables or formula can we get from what we have?

The problem looks fine to me. Just use the Lorentz force to calculate the value of the vertical E-field between the plates to balance the vertical deflection force from the magnetic field.

How do you calculate the velocity v of the proton as it enters the volume between the vertical plates? Be sure to be careful with your units as you change from eV to SI units for energy and velocity...

Which direction does the E-field between the vertical plates need to point to counter the vertical deflection force from the B-field? What magnitude does that E-field need to be?

EDIT/ADD -- Oh, and for good hygiene in problems like this, be sure to compare the velocity v that you get for the proton to the speed of light c. I suspect that the acceleration voltage that is specified is too low for v to be anywhere near c, but you always need to check. Can you say why it can be important for this type of problem if the particle has relativistic speed?

 

[Zero]

The problem looks fine to me. Just use the Lorentz force to calculate the value of the vertical E-field between the plates to balance the vertical deflection force from the magnetic field.

How do you calculate the velocity v of the proton as it enters the volume between the vertical plates? Be sure to be careful with your units as you change from eV to SI units for energy and velocity...

Which direction does the E-field between the vertical plates need to point to counter the vertical deflection force from the B-field? What magnitude does that E-field need to be?

EDIT/ADD -- Oh, and for good hygiene in problems like this, be sure to compare the velocity v that you get for the proton to the speed of light c. I suspect that the acceleration voltage that is specified is too low for v to be anywhere near c, but you always need to check. Can you say why it can be important for this type of problem if the particle has relativistic speed?

Unfortunately, I don't understand what you are saying. At the moment my class hasn't gone over Lorentz Force (at least I don't think we did) so I don't think that would apply. Also for the problem where would, I start or what value can I get from what I have. Lastly, I looked up Lorentz force and the formula I saw is F = qE + qv × B. which would not be usually since the only values we know are B and V making it have too many unknowns to solve.

 

[PeroK]

Unfortunately, I don't understand what you are saying. At the moment my class hasn't gone over Lorentz Force (at least I don't think we did) so I don't think that would apply. Also for the problem where would, I start or what value can I get from what I have. Lastly, I looked up Lorentz force and the formula I saw is F = qE + qv × B. which would not be usually since the only values we know are B and V making it have too many unknowns to solve.

You are given $F$. And $q$ is the charge on a proton. The only unknown is $\mathbf E$.

 

[berkeman]

I looked up Lorentz force and the formula I saw is F = qE + qv × B. which would not be usually since the only values we know are B and V making it have too many unknowns to solve.

As @PeroK says, since q is constant (what is the value of q for a proton? What is its mass?), the only unknown is E, which is what you are asked to solve for.

Much of what you wrote for equations in your Post #1 is based on the Lorentz Force equation. Are you comfortable with vector equations and calculating the cross product by using the Right-Hand Rule?

 

[Zero]

You are given $F$. And $q$ is the charge on a proton. The only unknown is $\mathbf E$.

Ok I'm finally understanding what you are trying to say but I still have one more question, wheres the F value in the statement given?

 

[haruspex]

Ok I'm finally understanding what you are trying to say but I still have one more question, wheres the F value in the statement given?

Here: such that the proton does not reflect and travels in a straight path.

 

[Zero]

Here: such that the proton does not reflect and travels in a straight path.

Ok i'll start guessing what it means, tell me if I'm correct, please. F is equal to 0 since the forces are balanced?

 

[haruspex]

Ok i'll start guessing what it means, tell me if I'm correct, please. F is equal to 0 since the forces are balanced?

Right. No acceleration, so no net force.

 

[Zero]

Right. No acceleration, so no net force.

Wow, thanks for the help everyone and sorry for my incompetence physics is not my strongest subject.

 

[berkeman]

Wow, thanks for the help everyone and sorry for my incompetence physics is not my strongest subject.

No worries at all, we are glad to help. We all learned the power of using the Lorentz force equation at some point in our education -- what a great vector (3-D) concept.