A particle with a charge of 31 µC moves with a speed of 62 m/s in the positive x-direction. The magnetic field in this region of space has a component of 0.50 T in the positive y-direction, and a component of 0.61 T in the positive z-direction. What is the magnitude and direction of the magnetic force on the particle?
magnitude:_______mN
degrees:________° (from the positive z-axis in the yz-plane)
This has been bothering me for a while. Any help is appreciated.
To find the magnitude and direction of the magnetic force on the particle, you can use the formula for the magnetic force experienced by a moving charged particle in a magnetic field:
F = q * v * B * sinθ
Where:
F is the magnetic force,
q is the charge of the particle,
v is the velocity of the particle,
B is the magnetic field,
and θ is the angle between the velocity vector and the magnetic field vector.
In this case, the charge of the particle is 31 µC (which can be converted to C by dividing by 10^6), the velocity is 62 m/s in the positive x-direction, the magnetic field has components of 0.50 T in the positive y-direction and 0.61 T in the positive z-direction.
First, we need to find the angle θ between the velocity vector and the magnetic field vector. Since the velocity is only in the x-direction, it is perpendicular to both the y and z-directions. Therefore, the angle between the velocity and the magnetic field is 90 degrees.
Now, let's plug these values into the formula:
F = (31 * 10^-6 C) * (62 m/s) * (0.50 T) * sin(90°)
The sin(90°) term is equal to 1, so the formula simplifies to:
F = (31 * 10^-6 C) * (62 m/s) * (0.50 T)
F = 0.0962 N
So the magnitude of the magnetic force is approximately 0.0962 N.
Since the magnetic field is in the positive y and z-directions, and the force is perpendicular to both the magnetic field and the velocity, the magnetic force will be in the negative x-direction. Therefore, the direction of the magnetic force is opposite to the positive x-direction.
In summary, the magnitude of the magnetic force is approximately 0.0962 N, and the direction of the magnetic force is opposite to the positive x-direction.