A positively charged particle is moving with a velocity v in a large homogeneous magnetic field.
(a) If the field is 4 mT, the mass of the particle is 33·10−9 kg, its initial speed 8.1 m/s, and its charge 6 μC, what is the magnitude of its acceleration? (in m/s^2)
(b) What is the speed of the particle 0.8 seconds later? (in m/s)
I figured out the answer for the first part. It is 5.9 m/s2... Still not sure how to get the answer to b though.
To solve this problem, we can use the equations of motion for a charged particle moving in a magnetic field.
(a) To find the magnitude of the acceleration, we can use the equation:
a = (q * v * B) / m
where:
- a is the acceleration
- q is the charge of the particle
- v is the velocity of the particle
- B is the magnetic field strength
- m is the mass of the particle
Substituting the given values into the equation, we have:
a = (6 * 10^-6 C * 8.1 m/s * 4 * 10^-3 T) / (33 * 10^-9 kg)
Simplifying this expression, we get:
a = 7.636 m/s^2
So, the magnitude of the acceleration is 7.636 m/s^2.
(b) To find the speed of the particle 0.8 seconds later, we can use the equation:
v' = v + a * t
where:
- v' is the final velocity
- v is the initial velocity
- a is the acceleration
- t is the time
Substituting the given values into the equation, we have:
v' = 8.1 m/s + 7.636 m/s^2 * 0.8 s
Calculating this expression, we get:
v' = 14.301 m/s
So, the speed of the particle 0.8 seconds later is 14.301 m/s.