A beam containing one hundred billion (i.e. 1x10^11) electrons moves perpendicula to a 4.0 Tesla magnetic field and is deflected by a 12 N force. (The electrons has a negative charge of 1.6 x 10^-19)
How much total charge is contained in the beam?
How quickly are these particles moving?
<<How much total charge is contained in the beam?>>
Q = 10^11 e, where e is the electron charge.
<<How quickly are these particles moving?>>
F = 12 N = Q V B
Solve for V, in m/s.
B = 4.0 T
To find the total charge contained in the beam, we need to determine the number of electrons in the beam. We are given that the beam contains 100 billion electrons, which can be expressed as 1x10^11 electrons.
The charge on each electron is given as 1.6x10^-19 C (coulombs). Therefore, to calculate the total charge in the beam, we multiply the charge on each electron by the number of electrons:
Total charge = (1x10^11 electrons) x (1.6x10^-19 C/electron)
Performing the calculation:
Total charge = 1x10^11 x 1.6x10^-19 C
= 1.6x10^-8 C
Thus, the total charge contained in the beam is 1.6x10^-8 Coulombs.
To find the speed at which these particles are moving, we can utilize the equation for the magnetic force acting on a charged particle:
F = qvB
Where:
F is the force (given as 12 N)
q is the charge of the particle (-1.6x10^-19 C for an electron)
v is the velocity of the particle (what we want to find)
B is the magnetic field strength (given as 4.0 T)
Rearranging the equation to solve for velocity:
v = F / (qB)
Substituting the given values:
v = 12 N / (-1.6x10^-19 C x 4.0 T)
= -12 N / (1.6x10^-19 C x 4.0 T)
= -12 N / (6.4x10^-19 C·T)
≈ -1.875x10^19 m/s
The negative sign indicates that the particles are moving in the opposite direction of the force (deflected in that direction) in this particular scenario. Therefore, the speed at which these particles are moving is approximately 1.875x10^19 meters per second.