Question

A vacuum chamber contains a uniform electric field directed downward. If a proton is shot horizontally into this region, it's acceleration is? Give direction and relative magnitude (Ex 45 degrees west of north, and is exponentially decreasing)

Answer 1

Answer:

It is directed downward. Its relative magnitude is a= qp*E/mp = 0.96*10⁸*E m/s².

Explanation:

Assuming  gravitational force to be negligible, the only force acting on the proton once within the vacuum chamber, is the one due to the electric field.

As the proton is a positive charge, the electric force on it due to the field has the same direction than the field, as the direction of the field by convention, is the one that would take a positive test charge.

According to electric field definition, and to Newton's 2nd Law, we can find the acceleration of the proton as follows:

F = m*a = q*E ⇒ a= q*E / m = 1.6*10⁻¹⁹ C * E (N/C) / 1.67*10⁻²⁷ kg

⇒ a = 0.96* 10⁸ * E m/s²