Question

Let’s say a very light magnetic point brush
and a uniform magnetic field generator are readily available. Design the apparatus in way that a user may opt to draw
small perfect circles, or big circles.

No idea how to do this as i am just starting in physics. thank you

Say you want to build a painting apparatus that draws a perfect circle. Lets say a very ligjt magnectic brush and uniform magnetic field generator are readily available. Desigm the apparatus in way that user may opt to draw small perfect circle or big circle

Answer 1

You know about the trajectory of a charged particle in a magnetic field. Let us consider - a charged particle of charge q is moving with a velocity of v perpendicularly to a uniform magnetic field B. The magnetic force will be

If the angle between the vectors v and B is 90^o, then you can write

And the path will be circular as the magnetic force will supply the centripetal force for the circular motion of the charged particle in a uniform magnetic field.

Let us consider that the radius of the circular path will be r. Therefore, you can write the expression for centripetal force and compare with magnetic force.

here, m is the mass of the charged particle. The radius of the circle will increase linearly with the velocity of the particle.

Here, in your problem, a point brush will act as a charged particle. If you project the brush with different speed and perpendicular the uniform magnetic field, you will get a perfect circle of different radius (drawing small perfect circles, or big circles).