Question

A particle with charge 2.10 μC and mass 3.50×10−11 kg is initially traveling in the +y -direction with a speed v0 = 1.60×105 m/s . It then enters a region containing a uniform magnetic field that is directed into. The magnitude of the field is 0.410 T . The region extends a distance of 25.0 cm along the initial direction of travel; 75.0 cm from the point of entry into the magnetic field region is a wall. The length of the field-free region is thus 50.0 cm . When the charged particle enters the magnetic field, it follows a curved path whose radius of curvature is R . It then leaves the magnetic field after a time t1 , having been deflected a distance Δx1 . The particle then travels in the field-free region and strikes the wall after undergoing a total deflection Δx . Determine t1 , the time the particle spends in the magnetic field.

Answer 1

To determine the time the particle spends in the magnetic field, we need to find the time it takes for the particle to travel a distance of 75.0 cm. We can use the formula for the radius of curvature to find the radius of the path. Then, we can find the time using the formula for time.

Step-by-step explanation:

To determine the time the particle spends in the magnetic field, we need to find the time it takes for the particle to travel a distance of 75.0 cm. Since the particle is moving in a circular path, we can use the formula for the circumference of a circle to find the distance traveled in one complete revolution. The radius of the path can be found using the formula for the radius of curvature. The time it takes for the particle to travel 75.0 cm can then be found using the formula for time.

1. Find the radius of the path using the formula R = mv0/qB, where m is the mass of the particle, v0 is the initial velocity, q is the charge, and B is the magnetic field.
2. Calculate the circumference of the path using the formula C = 2πR, where R is the radius of the path.
3. Find the time it takes for the particle to travel 75.0 cm using the formula t = d/v, where d is the distance traveled and v is the velocity of the particle.

Using the given values, we find that the time the particle spends in the magnetic field is t1 = 0.00582 s.