The Definition of B — Question 2

Question 2

An electron reverses the right-hand-rule force assigned to a positive charge

An electron with charge $-e$, where $e=1.602\times10^{-19}$ C, moves at $2.00\times10^6\hat x$ m/s in $.500\hat z$ tesla.

1. Find the magnetic force, including its direction.

2. Find the force if only the velocity is reversed and if both velocity and field are reversed.

Question 2 - Solution

An electron reverses the right-hand-rule force assigned to a positive charge

(a) Method and calculation

$$\hat x\times\hat z=-\hat y,\quad(-e)(v\hat x\times B\hat z)=evB\hat y.$$$$\vec F=1.602\times10^{-13}\hat y\,\mathrm N.$$

(b) Interpretation and further calculation

$$\vec F(-\vec v,\vec B)=-\vec F=-1.602\times10^{-13}\hat y\,\mathrm N.$$$$\vec F(-\vec v,-\vec B)=\vec F.$$

Physical check

Charge sign, velocity reversal and field reversal each change the force sign once; reversing two factors restores it.