A particle of mass 0.24kg and charge 2.0C istraveling due east. It entersperpendicularly a magnetic field whosemagnitude is 8.0 T. After entering the field, the particle completesone-half of a circle and exits the field traveling due west. How much timedoes the particle spend traveling in the magnetic field?
To find the amount of time the particle spends traveling in the magnetic field, we need to use the formula for the period of a charged particle moving in a magnetic field.
The formula for the period is given by:
T = (2 * π * m) / (|q| * B)
Where:
T = Period of the motion
m = Mass of the particle
q = Charge of the particle
B = Magnetic field strength
Given:
m = 0.24 kg
q = 2.0 C
B = 8.0 T
Plugging in the given values into the formula, we can calculate the period:
T = (2 * π * 0.24) / (|2.0| * 8.0)
First, we calculate the absolute value of charge |q| = |2.0| = 2.0
Now, we can plug in the values and calculate:
T = (2 * π * 0.24) / (2.0 * 8.0)
T = (2 * 3.1416 * 0.24) / (2.0 * 8.0)
T = (2 * 3.1416 * 0.24) / 16.0
T ≈ 0.0236 seconds
Therefore, the particle spends approximately 0.0236 seconds traveling in the magnetic field.