Some forms of cancer can be treated using proton therapy in...

Some forms of cancer can be treated using proton therapy in which proton beams are accelerated to high energies, then directed to collide into a tumor, killing the malignant cells. Suppose a proton accelerator is $4.0 \mathrm{m}$ long and must accelerate protons from rest to a speed of $1.0 \times 10^{7} \mathrm{m} / \mathrm{s} .$ Ignore any relativistic effects (Chapter 26 ) and determine the magnitude of the average electric field that could accelerate these protons.

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Key Concepts

Constant Acceleration Kinematics

This concept involves using kinematic equations for motion with constant acceleration, such as v² = 2ad, which relates the final speed, acceleration, and distance traveled. It is essential in determining how quickly a particle must accelerate over a given distance to reach a specific speed.

Newton’s Second Law and the Electric Force

Newton’s second law (F = ma) relates force to mass and acceleration. For charged particles, the force exerted by an electric field is given by F = qE. By combining these relationships, one can determine the required electric field strength to produce a given acceleration.

Work-Energy Principle in Charged Particle Acceleration

This principle entails that the work done by an electric field on a charged particle (force multiplied by distance) is converted into the kinetic energy of the particle. It provides an alternative method to calculate the necessary electric field by equating the work to the change in kinetic energy.

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