Homework Help: Electric fields/angle of deflection problem

1. Sep 19, 2006

oksanav

Here's the problem:
Ink-jet printers work by deflecting moving ink droplets with an electric field so they hit the right place on the paper. Droplets in a particular printer have mass 1 x 10^-10 kg, charge 2.1 pC, speed 12 m/s, and pass though a uniform 97-kN/C electric field in order to be deflected through a 10º angle. What is the length of the field region?

My teacher gave us this problem and there's only one like it in the book, and in that one angles aren't involved. My group worked it in class yesterday and he said we had the right idea but were misusing the angle. Our idea was to use kinematic equations, solve the y component for t and plug into the x component. The problem is we don't know what to do with the angle. We knew that the path starts with an angle of zero and is eventually 10º , but forgot this and were treating the angle as the initial angle. I just don't understand where the angle starts or how to treat it. Can I treat it as a triangle and somehow find the components of r(t)? Sorry to ramble on, I'm just frustrated.

2. Sep 19, 2006

Astronuc

Staff Emeritus
Well, one is given, the speed of 12 m/s, and one has the relationship the t = L/V, or L = Vt

In the same time, t, the droplet must accelerate to a distance, which is given by L tan(10°). One must fine the relationship between t and L tan(10°), or rather t in terms of L tan(10°), and substitute into L = Vt.

The angle between the axis of the inkjet and the spot on the paper must by 10°. That is the deflection when contact by ink drop on paper has been made.

Last edited: Sep 19, 2006