A beam of charged particles moving with a speed of 10⁶ m/s enters a uniform magnetic field of 0.1 T at right angles to the direction of motion. If the particles move in a radius of 0.2 m, then calculate their period of motion.

Question

Quizplus · Accepted Answer

The period of motion can be calculated using the equation T = 2πm/(qB), where m is the mass of the particle, q is its charge, and B is the magnetic field. In this case, we are not given the mass or charge of the particles, but we know that they are all moving with the same velocity, so we can assume that they have the same mass and charge.

Using the given radius and speed, we can calculate the magnetic field strength required to create the observed circular motion using the equation B = mv/(qr), where r is the radius of the circular path.

Plugging in the given values, we get B = (m)(10^16)/(q)(0.2), or B = 50m/q, where we have converted the velocity to meters per second.

Since we are told that the magnetic field is 0.1 T, we can equate these two expressions for B and solve for m/q:

0.1 T = 50m/q 
m/q = (0.1 T)/(50) = 2 × 10^-3 kg/C

Now we can plug this value for m/q into the equation for the period of motion:

T = 2πm/(qB) = 2π(m/q)/(B) = 2π/(B(m/q))

Substituting in the known values, we get T = 2π/(0.1 T)(2 × 10^-3 kg/C) = 1.3 × 10^-6 s, or C.

A Beam of Charged Particles Moving with a Speed of 106

A Beam of Charged Particles Moving with a Speed of 10⁶