PhysicsBowl 2018 Q37

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PhysicsBowl 2018

37) This question asks us to find the force acting on the electron traveling through a magnetic field. The magnitude of the magnetic force produced by a magnetic field can be expressed with this equation.

Where F[B] is magnetic force, q is charge, v is velocity, and B is magnetic field

Here we are using the cross-product of v and B, which means that we want only the components of v and B that are perpendicular to each other. This question is only concerned with the magnitude of the magnetic force, so we can rewrite this expression.

Where F[B] is magnetic force, q is charge, v is velocity, and B is magnetic field, and θ is the angle between velocity and magnetic field

Next, let's draw a diagram to visualize this problem.

Where blue represents electrons, v is velocity, and B is magnetic field

Finally, we can go ahead and plug in all the necessary values to the formula. We can see that by using B*sin(45), we will get the component of the magnetic field that is perpendicular to the velocity.

Also remember that the particle is an electron, so its charge is a known constant.

Where F[B] is magnetic force, q is charge, v is velocity, and B is magnetic field, and θ is the angle between velocity and magnetic field

Answer: A