AP Physics 2 Exam Question - Particle Physics
Consider a particle accelerator that is designed to accelerate protons to high speeds. The protons are initially at rest and are accelerated through an electric potential difference of 2.0 MV. After being accelerated, the protons have a final kinetic energy of 1.5 GeV.
Determine the charge on a proton in coulombs. (Given: elementary charge, e = 1.60 x 10^-19 C)
Calculate the potential difference in volts that can achieve a proton kinetic energy of 1.5 GeV. (Given: 1 GeV = 1.60 x 10^-10 J)
Explain why accelerating the protons through a higher potential difference would result in an increase in their final kinetic energy.
If the interparticle distance within the proton accelerator is 0.5 m, calculate the electric field strength within the accelerator in newtons per coulomb (N/C).
Answer with Step-by-Step Explanation
The charge on a proton can be calculated using the given elementary charge.
Charge on a proton = elementary charge (e) = 1.60 x 10^(-19) C
The charge on a proton is 1.60 x 10^(-19) C.
To calculate the required potential difference (V), we can use the formula:
Kinetic energy (K) = qV
Rearranging the formula, V = K / q
The proton's kinetic energy is given as 1.5 GeV. Converting 1.5 GeV to joules:
1.5 GeV = 1.5 x 1.60 x 10^(-10) J = 2.40 x 10^(-10) J
Plugging the values into the formula, V = (2.40 x 10^(-10) J) / (1.60 x 10^(-19) C)
V ≈ 1.50 x 10^9 V
The potential difference required to achieve the given proton kinetic energy is approximately 1.50 x 10^9 V.
When protons are accelerated through a higher potential difference, they gain more kinetic energy. This is because the potential difference is directly related to the work done on the charged particle. The work done by the electric field on a charged particle is given by the equation:
Work (W) = qV
Therefore, increasing the potential difference results in more work done on the protons, which in turn increases their kinetic energy.
The electric field strength (E) within the accelerator can be calculated using the formula:
Electric field strength (E) = V / d
Plugging in the values, E = (1.50 x 10^9 V) / (0.5 m)
E = 3.00 x 10^9 N/C
The electric field strength within the proton accelerator is approximately 3.00 x 10^9 N/C.