1.)A proton moving with speed v enters a narrow (1.0 cm wide) region of magnetic field perpendicular to the direction of the proton's motion. As a result, the proton acquires a small component of speed perpendicular to its original direction of motion. This speed is much less than the original speed, and is measured to be 3.3 x10 ^5 m/s. The magnitude of the force on the proton is 1.8 x10 ^-18 N. What is the strength of the magnetic field?
Force=B*l*v You are given force, length, and velocity. solve for B
1.)A proton moving with speed v enters a narrow (1.0 cm wide) region of magnetic field perpendicular to the direction of the proton's motion. As a result, the proton acquires a small component of speed perpendicular to its original direction of motion. This speed is much less than the original speed, and is measured to be 3.3 x10 ^5 m/s. The magnitude of the force on the proton is 1.8 x10 ^-18 N. What is the strength of the magnetic field?
To find the strength of the magnetic field, we can use the formula for the magnetic force on a moving charged particle:
F = qvB
where F is the force, q is the charge of the particle, v is the velocity, and B is the magnetic field strength.
In this case, the force is given as 1.8 x 10^-18 N, and the speed of the proton perpendicular to its original motion is given as 3.3 x 10^5 m/s.
The charge of a proton is equal to the elementary charge, e, which is 1.6 x 10^-19 C.
Substituting these values into the formula, we get:
1.8 x 10^-18 N = (1.6 x 10^-19 C)(3.3 x 10^5 m/s)(B)
Solving for B, we have:
B = (1.8 x 10^-18 N) / [(1.6 x 10^-19 C)(3.3 x 10^5 m/s)]
B ≈ 3.491 x 10^-4 T
Therefore, the strength of the magnetic field is approximately 3.491 x 10^-4 Tesla.
To find the strength of the magnetic field, we can use the formula for the magnetic force on a charged particle moving through a magnetic field:
F = q * v * B
Where:
- F is the force on the charged particle
- q is the charge of the particle (in this case, the charge of a proton, which is 1.6 x 10^-19 C)
- v is the velocity of the particle
- B is the strength of the magnetic field
In this case, we are given the force on the proton (1.8 x 10^-18 N) and the velocity of the proton after entering the magnetic field (3.3 x 10^5 m/s).
1. Rearrange the formula to solve for B:
B = F / (q * v)
2. Substitute the given values:
B = (1.8 x 10^-18 N) / ((1.6 x 10^-19 C) * (3.3 x 10^5 m/s))
3. Calculate the result:
B = (1.8 x 10^-18) / (1.6 x 10^-19 * 3.3 x 10^5)
B = approximately 3.4 x 10^-5 T (Tesla)
Therefore, the strength of the magnetic field is approximately 3.4 x 10^-5 Tesla.