What is the acceleration of a proton moving with a speed of 4.3 m/s at right angles to a magnetic field of 2.1 T?
To find the acceleration of a proton moving in a magnetic field, we can use the equation for the magnetic force acting on a charged particle:
F = q * v * B
where:
F is the magnetic force,
q is the charge of the particle,
v is the velocity of the particle, and
B is the magnetic field strength.
In this case, we are given:
v = 4.3 m/s (velocity of the proton),
B = 2.1 T (magnetic field strength), and
q = charge of a proton = 1.6 * 10^-19 C.
Now, we can substitute these values into the equation:
F = (1.6 * 10^-19 C) * (4.3 m/s) * (2.1 T)
Next, we can find the acceleration of the proton using Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration:
F = m * a
Since the mass of a proton is approximately 1.67 * 10^-27 kg, we can rearrange the formula to solve for acceleration:
a = F / m
Now, by substituting the calculated magnetic force and proton mass into this equation, we can find the acceleration:
a = [(1.6 * 10^-19 C) * (4.3 m/s) * (2.1 T)] / (1.67 * 10^-27 kg)
Simplifying this calculation will give us the acceleration of the proton.