A particle of mass 0.24kg and charge 2.0C is traveling due east. It enters perpendicularly a magnetic field whose magnitude is 8.0 T. After entering the field, the particle completes one-half of a circle and exits the field traveling due west. How much time does the particle spend traveling in the magnetic field?
To calculate the time the particle spends traveling in the magnetic field, we can use the formula:
t = θ / ω
Where:
t is the time,
θ is the angle the particle travels,
and ω is the angular velocity.
In this case, we know that the particle completes one-half of a circle, which means it travels 180 degrees or π radians.
The angular velocity (ω) of a charged particle moving in a magnetic field can be calculated using the formula:
ω = qB / m
Where:
ω is the angular velocity,
q is the charge of the particle,
B is the magnitude of the magnetic field,
and m is the mass of the particle.
Given:
q = 2.0 C (charge of the particle)
B = 8.0 T (magnitude of the magnetic field)
m = 0.24 kg (mass of the particle)
Let's calculate the angular velocity:
ω = (2.0 C * 8.0 T) / 0.24 kg
ω = 16.0 C⋅T / 0.24 kg
ω = 66.7 rad/s (rounded to 3 significant figures)
Now, we can calculate the time:
t = θ / ω
t = π rad / 66.7 rad/s
t ≈ 0.047 s (rounded to 3 decimal places)
Therefore, the particle spends approximately 0.047 seconds traveling in the magnetic field.