A beam of electrons moves at right angles to a magnetic field of 7.2 multiplied by 10-2 T. The electrons have a velocity of 2.5 multiplied by 106 m/s. What is the magnitude of the force on each electron?
F=Bqv right?
F=7.2E-2 * 1.6E-19 *2.5E6
check that
To find the magnitude of the force on each electron, we can use the formula for the magnetic force on a charged particle moving in a magnetic field. The formula is given by:
F = q * v * B * sin(θ)
Where:
F is the magnetic force on the particle,
q is the charge of the particle (in this case, the charge of an electron which is -1.6 × 10^-19 C),
v is the velocity of the particle,
B is the magnetic field strength, and
θ is the angle between the velocity vector and the magnetic field vector.
In this case, the velocity of the electrons is directed at a right angle (90 degrees) to the magnetic field. Therefore, sin(90 degrees) = 1.
Plugging in the given values:
q = -1.6 × 10^-19 C (charge of an electron),
v = 2.5 × 10^6 m/s (velocity of the electrons),
B = 7.2 × 10^-2 T (magnetic field strength), and
θ = 90 degrees.
Using these values in the formula, we can calculate the magnitude of the force on each electron:
F = (-1.6 × 10^-19 C) * (2.5 × 10^6 m/s) * (7.2 × 10^-2 T) * sin(90 degrees)
Calculating this expression:
F = (-1.6 × 10^-19 C) * (2.5 × 10^6 m/s) * (7.2 × 10^-2 T) * 1
F = -3.6 × 10^-13 N
Therefore, the magnitude of the force on each electron is 3.6 × 10^-13 N.