#### Projectile Motion

If you threw a mass through the air it would follow a parabolic path because of gravity. You could determine when and where the object would land by doing a projectile motion analysis, separating everything into x and y components. The horizontal acceleration is zero, and the vertical acceleration is g. We know this because a free-body diagram shows only mg, acting vertically, and applying Newton's second law tells us that mg = ma, so a = g.

Similarly, if you throw a charge into a uniform electric field (same magnitude and direction everywhere) and neglect gravity, the charge would also follow a parabolic path. The acceleration is zero in one direction and constant in the other. The value of the acceleration can be found by drawing a free-body diagram (one force, F = qE) and applying Newton's second law. This says:

qE = ma, so the acceleration is a = qE / m.

Is it valid to neglect gravity? What matters is the size of qE / m relative to g. As long as qE / m is much larger than g, gravity can be ignored. Gravity is very easy to account for, of course : simply add mg to the free-body diagram and go from there.

The one big difference between gravity and electricity is that m, the mass, is always positive, while q, the charge, can be positive, zero, or negative.