Electric field and magnetic field acting simultaneously on a charged particle

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Discussion Overview

The discussion revolves around a physics problem involving the motion of an electron subjected to both electric and magnetic fields. Participants explore the application of the Lorentz force law to determine the electric field acting on the electron given its initial velocity and acceleration.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant presents a problem involving an electron with specific initial velocity and acceleration in uniform electric and magnetic fields, expressing uncertainty about how to approach the problem with both fields acting simultaneously.
  • Another participant introduces the Lorentz force law, suggesting it as a starting point for solving the problem.
  • A participant describes their process of substituting known values into the Lorentz force equation and solving for the electric field, arriving at a specific value for E.
  • There is a correction regarding the sign of the electron's charge, which leads to a revision of the calculated electric field components.
  • One participant acknowledges their mistake in the calculation and provides a revised answer for the electric field, indicating a change in the signs of the components.

Areas of Agreement / Disagreement

Participants engage in a back-and-forth regarding the calculations and corrections, with some agreement on the application of the Lorentz force law, but no consensus on the final value of the electric field until the last post, where one participant acknowledges their error.

Contextual Notes

There are unresolved aspects regarding the initial assumptions made in the calculations and the implications of the charge's sign on the final results.

mfoley14
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The problem that I'm working on states: "An electron has initial velocity (12j +15k)km/s and a constant accelaration of (2.0 x 10^12 i) m/s^2 in a region of uniform electric and magnetic field. If B equals 400i microTeslas, find electric field E.

I know how to do most of the components of this problem, for example a particle traveling through a magnetic field or an electric field. However, I'm not sure where exactly to begin when addressing a particle which has both E and B acting on it.
 
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mfoley14 said:
The problem that I'm working on states: "An electron has initial velocity (12j +15k)km/s and a constant accelaration of (2.0 x 10^12 i) m/s^2 in a region of uniform electric and magnetic field. If B equals 400i microTeslas, find electric field E.

I know how to do most of the components of this problem, for example a particle traveling through a magnetic field or an electric field. However, I'm not sure where exactly to begin when addressing a particle which has both E and B acting on it.

Hi mfoley14! Welcome to MHB! (Smile)

The Lorentz force in the presence of both an electric and a magnetic field is:
$$\mathbf F =q (\mathbf E + \mathbf v \times \mathbf B)$$
How far can you get with that?
 
Using the Lorentz Force Law, I was able to sub out components of the formula with known values. I solved for f using the accelaration and the mass of an electron, substituted the charge of an electron for q, and found the cross product of v and B. So, f = q(E + v x B) became (9.1x10^-31)(2x10^12)i = (1.6x10^-19)(E +6j - 4.8k). I then solved for E and found that E = 11.375 i -6 j + 4.8 k Newtons per coulomb. Is this correct?
 
mfoley14 said:
Using the Lorentz Force Law, I was able to sub out components of the formula with known values. I solved for f using the accelaration and the mass of an electron, substituted the charge of an electron for q, and found the cross product of v and B. So, f = q(E + v x B) became (9.1x10^-31)(2x10^12)i = (1.6x10^-19)(E +6j - 4.8k). I then solved for E and found that E = 11.375 i -6 j + 4.8 k Newtons per coulomb. Is this correct?

Almost!
The charge of an electrion is $-1.6\cdot10^{-19}\textrm{ C}$ .
Note the minus sign that effectively reverses the Lorentz force.
 
I knew that! Adding the negative sign to my calculation only switches the sign of each component, so the correct answer I believe is E = -11.375 i + 6 j -4.8 k
 
mfoley14 said:
I knew that!

Good!

Adding the negative sign to my calculation only switches the sign of each component, so the correct answer I believe is E = -11.375 i + 6 j -4.8 k

Erm... it only switches the sign of the x component.
 
Wow that was some lazy math on my part. I spotted my mistake. E = -11.375 i - 6 j + 4.8 k.
Thank you for your help!
 

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