Question

An electron is moving through a magnetic field whose magnitude is 9.79

Answer 1

An electron is a charged particle. For charged particles moving in a magnetic field we have the Lorentz force law:

where q is the charge, E is the electric field (in this case it's zero), is the velocity of the particle and B is the magnetic field. Note that there is a VECTOR product between the velocity and the magnetic field. Also, remember Newton's SEcond law:

Recall that the magnitudeof any vector product is: where A and B are the magnitudes of the vectors and is the angle between them.

In our case: There's only one force: the magnetic force, therefore:

that is: Which is just :

Take magnitudes on both sides: () and apply the property f the magnitude of a vector product:

where everything is now in magnitudes. Remember that speed is the magnitude of the velocity vector. Solve for . Therefore: . This is the angle (less than ) that has sine equal to . Plugging in values, remember that the mass and charge of the electron is and the other three values are given:

(with a calculator, where arcsin usually appears as ""