A proton, traveling with a velocity of 4.9 106 m/s due east, experiences a magnetic force that has a maximum magnitude of 7.4 10-14 N and a direction of due south. What are the magnitude and direction of the magnetic field causing the force?
To determine the magnitude and direction of the magnetic field causing the force on the proton, we can use the formula for the magnetic force on a charged particle:
F = q * v * B * sin(theta)
where:
F is the magnetic force on the particle
q is the charge of the particle (in this case, the charge of a proton = 1.6 x 10^-19 C)
v is the velocity of the particle (4.9 x 10^6 m/s due east)
B is the magnetic field
theta is the angle between the velocity vector and the magnetic field vector.
From the given information, we know:
F = 7.4 x 10^-14 N
q = 1.6 x 10^-19 C
v = 4.9 x 10^6 m/s due east
theta (angle between the velocity vector and the magnetic field vector) = 90 degrees (since the force is directed due south).
Now, we can rearrange the equation to solve for the magnetic field (B):
B = F / (q * v * sin(theta))
Substituting the values we know:
B = (7.4 x 10^-14) / ((1.6 x 10^-19) * (4.9 x 10^6) * sin(90))
After evaluating this expression, we find:
B ≈ 3.73 x 10^-5 T
So, the magnitude of the magnetic field causing the force on the proton is approximately 3.73 x 10^-5 Tesla.
Since the force is directed due south, we know that the magnetic field is directed due north, as magnetic fields always act perpendicular to the direction of the force on a charged particle.
To find the magnitude and direction of the magnetic field, we can use the formula for the magnetic force on a moving charged particle:
F = qvBsinθ
Where:
- F is the magnetic force
- q is the charge of the particle (in this case the charge of a proton = 1.6 x 10^-19 C)
- v is the velocity of the particle
- B is the magnitude of the magnetic field
- θ is the angle between the velocity vector and the magnetic field vector
Given:
- F = 7.4 x 10^-14 N
- q = 1.6 x 10^-19 C
- v = 4.9 x 10^6 m/s
- θ = 90 degrees (due east and due south are perpendicular)
Substituting the given values into the formula, we can solve for B:
7.4 x 10^-14 N = (1.6 x 10^-19 C)(4.9 x 10^6 m/s)(B)(sin 90°)
Simplifying the equation:
B = (7.4 x 10^-14 N) / [(1.6 x 10^-19 C)(4.9 x 10^6 m/s)]
B ≈ 2.4 x 10^-4 T
So, the magnitude of the magnetic field is approximately 2.4 x 10^-4 T.
The direction of the magnetic field can be determined using the right-hand rule. Since the magnetic force is directed due south, placing your right hand in the direction of the velocity (due east), with your fingers extended, your thumb will point in the direction of the magnetic field.
Therefore, the direction of the magnetic field is due south.