A charged particle with charge q is moving with speed v in a uniform magnetic field. A second identical charged particle is moving with speed 2v perpendiculuar to the same magnetic field. The time to complete one full circular revolution for the first particle T1. The time to complete one full circular revolution for the particle moving with speed 2v
is T1/4 b. T1/2 c. T1 4. 2T1 e.4T1
F=qvB
mv²/R=qvB
R=mv/qB
T=2πR/v=2π mv/qBv=
=2π m/qB
T1=T2 (T doesn’t depend on v)
Hi Elena, I got that too, hope it's the right answer
To find the time taken for each particle to complete one full circular revolution, we can use the formula for the period of circular motion in a magnetic field. The formula is given by:
T = (2πm)/(qB)
where T is the period, m is the mass of the particle, q is its charge, and B is the magnetic field strength.
Since both particles have identical charges and are in the same magnetic field, the only difference is their velocities. Let's calculate the periods for both particles separately:
For particle 1:
T1 = (2πm)/(qv)
For particle 2:
T2 = (2πm)/(q(2v))
Simplifying the expressions:
T1 = (2πm)/(qv)
T2 = (2πm)/(2qv)
T2 = (1/2)(2πm)/(qv)
T2 = (1/2)T1
Therefore, the time taken for the particle moving with speed 2v to complete one full circular revolution is half the time taken by the particle moving with speed v.
So, the correct answer is option b) T1/2
To find the time taken for one full circular revolution for each particle, we can use the formula for the period of a circular motion in a magnetic field.
The period of circular motion in a magnetic field is given by the equation:
T = 2πm / qB
Where:
T is the period (time taken for one full circular revolution),
m is the mass of the charged particle,
q is the charge of the particle,
B is the magnetic field strength.
In this case, we are given that the two particles are identical, so their masses (m) and charges (q) are the same.
Let's denote the time for the first particle T1.
For the first particle:
T1 = 2πm / qB
For the second particle moving with speed 2v perpendicular to the same magnetic field, we can use the fact that the time for a circular motion is inversely proportional to the velocity.
Since the second particle has a velocity twice that of the first particle, it completes the circular motion in half the time.
So, for the second particle:
T2 = T1 / 2
Comparing the given options, we can see that option (b) T1/2 matches the time T2 taken for the second particle to complete one full circular revolution.