An electron is accelerated through 2300 V from rest and then enters a uniform 1.90 T magnetic field.
(a) What is the maximum value of the magnetic force this charge can experience?
(b) What is the minimum value this charge can experience?
To find the maximum and minimum values of the magnetic force experienced by an electron, we'll need to use the equations for electric and magnetic forces.
(a) The maximum value of the magnetic force can be obtained when the velocity of the electron is perpendicular to the magnetic field. In this case, the force can be calculated using the formula:
F = qvBsinθ
Where:
- F is the force experienced by the electron
- q is the charge of the electron (1.6 x 10^-19 C)
- v is the velocity of the electron
- B is the magnetic field strength (1.90 T)
- θ is the angle between the velocity vector and the magnetic field vector (which is 90 degrees when the velocity is perpendicular to the magnetic field)
Now, let's solve for the velocity of the electron using the given voltage:
V = ∆PE/q
Where:
- V is the voltage (2300 V)
- ∆PE is the change in potential energy (which is equal to the kinetic energy at the max point)
- q is the charge of the electron (1.6 x 10^-19 C)
The potential energy at the max point is given by:
∆PE = qV
Substituting the values, we can solve for the velocity:
V = ∆PE/q
2300 V = (1.6 x 10^-19 C) * v
v = 2300 V * (1 C / (1.6 x 10^-19 C))
v = 1.44 x 10^23 m/s
Now that we have the velocity, we can calculate the maximum magnetic force:
F = qvBsinθ
F = (1.6 x 10^-19 C) * (1.44 x 10^23 m/s) * (1.90 T) * sin(90 degrees)
F ≈ 4.60 x 10^-15 N
So the maximum value of the magnetic force the charge can experience is approximately 4.60 x 10^-15 Newtons.
(b) The minimum value of the magnetic force occurs when the velocity of the electron is parallel to the magnetic field (θ = 0 degrees). In this case, the force experienced by the electron will be zero since sin(0 degrees) = 0.
Therefore, the minimum value of the magnetic force that the charge can experience is zero.