An electron in a television CRT moves toward the front of the tube with a speed of 7.5x10^6 m/s. A magnetic field of 0.04T (on a 50 degrees angle) causes the electrons to accelerate. Determine the acceleration
F=ma=evBsinα
a= evBsinα/m =1.6•10⁻¹⁹•7.5•10⁶•0.04•sin50/9.1•10⁻³¹= 4•10¹⁶ m/s²
To determine the acceleration of the electron, we can use the principles of electromagnetism and the formula for the magnetic force on a moving charged particle.
The formula for the magnetic force on a moving charged particle is given by:
F = q * v * B * sin(theta)
Where:
F is the magnetic force
q is the charge of the particle
v is the velocity of the particle
B is the magnetic field strength
theta is the angle between the velocity and the magnetic field
In this case, the charge of the electron, q, is -1.6 x 10^-19 C (Coulombs), the velocity of the electron, v, is 7.5 x 10^6 m/s, the magnetic field strength, B, is 0.04 T (Tesla), and the angle, theta, is 50 degrees.
First, we need to convert the angle from degrees to radians because the sine function in the formula expects the angle to be in radians.
theta (in radians) = theta (in degrees) * (π / 180)
Using this conversion, we have:
theta (in radians) = 50 * (π / 180) = 0.8727 radians
Now we can substitute the values into the formula:
F = (-1.6 x 10^-19 C) * (7.5 x 10^6 m/s) * (0.04 T) * sin(0.8727 radians)
Calculating this expression gives us the value of the magnetic force, F.
To calculate the acceleration, we can use Newton's Second Law, which states that the force acting on an object is equal to its mass times its acceleration:
F = m * a
Rearranging the formula to solve for acceleration, we get:
a = F / m
The mass of an electron is approximately 9.11 x 10^-31 kg.
Now we can substitute the values into this formula to calculate the acceleration:
a = F / m = (calculated value of F) / (9.11 x 10^-31 kg)
Evaluating this expression will provide you with the acceleration of the electron caused by the magnetic field.