Question

8. The voltage applied to a 10m-long linear particle accelerator is given by the following relation, V(x) = (3000 - 5x^2 m^-2)V , where x is the distance from the left plate along the accelerator tube, as show in the figure below. The mass of the proton is 1.67 · 10^-27 kg . (a) Using energy conservation, determine an expression for the kinetic energy of a charged particle, q0, released from rest at x=0, as a function of x, if the particle is moving along the x-axis in this accelerator. Calculate the speed of the particle for x=4m, if the particle is a proton. (b) Using the given potential function, determine the electric field as a function of x within the accelerator tube and calculate the acceleration of the proton at x=4m.

          8. The voltage applied to a 10m-long linear particle accelerator is given by the following relation, V(x) = (3000 - 5x^2 m^-2)V , where x is the distance from the left plate along the accelerator tube, as show in the figure below. The mass of the proton is 1.67 · 10^-27 kg .

(a) Using energy conservation, determine an expression for the kinetic energy of a charged particle, q0, released from rest at x=0, as a function of x, if the particle is moving along the x-axis in this accelerator. Calculate the speed of the particle for x=4m, if the particle is a proton. (b) Using the given potential function, determine the electric field as a function of x within the accelerator tube and calculate the acceleration of the proton at x=4m.

8. The voltage applied to a 10m-long linear particle accelerator is given by the following relation, V(x) = (3000 - 5x^2 m^-2)V , where x is the distance from the left plate along the accelerator tube, as show in the figure below. The mass of the proton is 1.67 · 10^-27 kg .

(a) Using energy conservation, determine an expression for the kinetic energy of a charged particle, q0, released from rest at x=0, as a function of x, if the particle is moving along the x-axis in this accelerator. Calculate the speed of the particle for x=4m, if the particle is a proton. (b) Using the given potential function, determine the electric field as a function of x within the accelerator tube and calculate the acceleration of the proton at x=4m.

Added by Edward S.

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