A positive ion is shot between the plates of a parallel-plate capacitor as shown

Question

A positive ion is shot between the plates of a parallel-plate capacitor as shown. (a.) In what direction is the electric force on the ion? Explain. (b.) A magnetic field (not shown) exerts a magnetic force on the ion that is equal but opposite to the electric force. If that magnetic field has the smallest possible magnitude, what is its direction? Explain. (c.) If gravity can be ignored, derive an equation for the magnitude of that field in terms of the electric field. (d.) In what direction would the ion need to be moving in order to make it impossible for the magnetic force to cancel the electric force? Explain.

Explanation / Answer

According to the question

We know that,

A) upper plate is +ve charged and lower plate is -ve charged.

hence field will be downward.

and electric force, Fe = q E
so electric force on ion (ion is +ve) will be downward.

Then,

B) magnetic force will be uwpard. and ion is moving to the right.

magnetic force = q (v x B)

so direction of B will be into the page.

Then,

C) Fe = Fm

q E = q v B

B = E/v

where v is the moving speed of ion.

Then,

D) ion have to move always to right to cancel the force.

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