What Magnetic Field Strength Keeps an Electron on a Straight Path?

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Homework Help Overview

The problem involves an electron accelerated through a potential difference and entering a region between parallel plates with a specified potential difference. The objective is to determine the uniform magnetic field strength that allows the electron to maintain a straight trajectory within the gap, considering the forces acting on it.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between the forces acting on the electron, particularly the balance between magnetic and electric forces. There is an exploration of relevant equations, including the kinetic energy gained from the potential difference and the forces involved in maintaining a straight path.

Discussion Status

Some participants have provided guidance on the equations to use and the relationships between the forces. There is an ongoing exploration of how to calculate the electron's velocity and how to apply it to find the magnetic field strength. Multiple interpretations of the problem setup and the equations are being discussed.

Contextual Notes

Participants note the need to consider the effects of potential differences and the assumptions made about the electron's motion, including neglecting fringing effects and the perpendicularity of velocity and electric field vectors.

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Homework Statement



In the figure, an electron accelerated from rest through potential difference 1.7 kV enters the gap between two parallel plates having separation 20.0 mm and potential difference 110 V. The lower plate is at the lower potential. Neglect fringing and assume that the electron's velocity vector is perpendicular to the electric field vector between the plates. What uniform magnetic field allows the electron to travel in a straight line in the gap?


Homework Equations


F=qvB
q=charge
v=velocity
B=magnetic field




The Attempt at a Solution



I honestly don't know where to even begin, I know I've got to be missing a formula because distance has got to be used somewhere in there, I'm just interested in getting an idea how to start this problem.
 
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If the electron travels in a straight line it doesn't accelerate upwards/downwards, which essentially means that the sum of all forces acting in the direction of the y-axis is zero. The magnetic force has to be equal, but opposite to that of the electric force.
 
Ok, so that means that F=-F, and i found another formula qvB=(mv^2)/r, but I'm sure that I need to find the velocity first and then use that and substitute and since i have two equations i would be able to solve for F which would allow me to find B, but I'm not sure how to find the velocity by only knowing the potential differences.
 
Forget qvB=(mv^2)/r. This equation describes an electron (or any other particle with a charge q) moving in a circular path, this is not true in your assignment.

If a particle with the charge q is accelerated with the voltage U it will gain kinetic energy according to

qU=\frac{1}{2}mv^2

From this equation you can solve the speed of the electron.
 
Ok so, I found the velocity to be 24,449 m/s and then by combining the equations qvB=F and F=qE I got the equation vB=E so 24449 m/s x B = E and E=V(volts) / d

so I plugged in numbers and 1.27e-10 but wrong... Is my math wrong?
 

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