The electron gun in a color TV accelerates the electrons through about 25,000 Volts. Estimate the acceleration of such an electron due to the magnetic field of the earth. Hint: In Atlanta, the Earth's magnetic field has a magnitude of about 5.2 X 10-5 T.
The force on the electron is
F = e V B,
where V is the velocity and e is the electron charge. Get the velocity V from the energy.
(1/2) m V^2 = 25,000 V * e
Divide the force F by the electron mass m to get the acceleration.
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To estimate the acceleration of an electron due to the magnetic field of the Earth, we can use the formula for the magnetic force experienced by a charged particle moving in a magnetic field:
F = q * v * B
where F is the magnetic force, q is the charge of the particle, v is its velocity, and B is the magnetic field strength.
In this case, the electron has a charge of -1.6 x 10^-19 C (coulombs) and we need to find the acceleration, so we need to rearrange the formula to solve for acceleration:
F = m * a (Newton's second law)
q * v * B = m * a
Divide both sides by the mass of the electron (m = 9.11 x 10^-31 kg) to solve for acceleration (a):
a = (q * v * B) / m
Now, let's substitute the given values into the formula.
q = -1.6 x 10^-19 C
v = unknown (velocity of the electron in the TV)
B = 5.2 x 10^-5 T
m = 9.11 x 10^-31 kg
We need to find the velocity (v) of the electron corresponding to an acceleration of 25,000 Volts.
To find the velocity, we can use the formula for kinetic energy:
K.E. = (1/2) * m * v^2
In this case, the kinetic energy is given by the voltage (25,000 Volts), and we can rearrange the formula to solve for velocity (v):
v = √((2 * K.E.) / m)
Now, let's substitute the given values into the formula.
K.E. = 25,000 V
m = 9.11 x 10^-31 kg
Now we can substitute the velocity (v) into the formula for acceleration.
a = (q * v * B) / m
Finally, calculate the acceleration:
a = (-1.6 x 10^-19 C * v * 5.2 x 10^-5 T) / (9.11 x 10^-31 kg)
Note that you will need to substitute the calculated velocity (v) into this formula to determine the estimated acceleration of the electron due to the Earth's magnetic field.