Consider an electron entering a region between two charged metal plates where, aside from the electric field E, there is also a constant magnetic field B directed into the paper. V is the velocity of the electron (from left to right direction).
a)Write an expression for the electric and magnetic force.
b) It is observed that if B= 1.5 T and E=5.5 x 10^3 V/m, the electron keeps moving in a straight line. Find the speed of the electron (Assume there is no effect of gravity)
a) The electric force is e E, in the drection of the positive plate. The magnetic force is e V B, perpendicular to V and B
b) If the electron is moving parallel to the plates, the B force and E force can be in opposite directions, cancelling each other out when V*B = E
V = E/B = 3670 m/s
a) To write an expression for the electric and magnetic force experienced by the electron, we need to consider that the electric force will be given by Coulomb's Law and the magnetic force will be given by the Lorentz force equation.
1. Electric Force (Fe):
The electric force experienced by a charged particle in an electric field is given by:
Fe = q * E
where
Fe is the electric force,
q is the charge of the electron (1.6 x 10^-19 C) since it is negative,
E is the electric field strength.
2. Magnetic Force (Fm):
The magnetic force experienced by a charged particle moving in a magnetic field is given by the Lorentz force equation:
Fm = q * (V x B)
where
Fm is the magnetic force,
q is the charge of the electron,
V is the velocity of the electron,
B is the magnetic field,
x represents the vector cross product.
Note: In this case, the force from the magnetic field is acting perpendicular to the velocity, so it will only cause the electron to move in a circular path, rather than changing its speed.
b) To find the speed of the electron when it moves in a straight line, we need to equate the electric force and magnetic force to zero since the electron is not experiencing any net force perpendicular to its velocity. This can be written as:
Fe = Fm
q * E = q * (V x B)
Canceling out the charge (q) on both sides, we have:
E = V x B
Now we can calculate the speed of the electron.