Static Electricity Legacy Problem #21 Guided Solution

This is a good example of a problem that has very little difficulty in terms of its mathematical rigor, yet can cause considerable difficulty to a student if they're not understanding the concept. So, the take-home message here is always have understanding of your concepts as you approach mathematical problems. It's not just a matter of knowing the formula, it's a matter of knowing the concept so that you can determine the formula. So here we wish to calculate the force and the acceleration of an electron that's traveling through an electric field. It happens to be an electric field created by a cathode ray tube on an old television set. And we know the electric field value is 2.5 times 10 to the 4th Newtons per Coulomb. What that tells us is, as an electron or any charged object travels through those little electric field plates, or those little parallel plates of the cathode ray tube, that every one Coulomb of charge would experience 2.4 times 10 to the 4th Newtons of force. We don't nearly have a Coulomb of charge here, and what we have is the charge on a single electron, 1.60 times 10 to the negative 19th. And so if we wish to find the force that acts upon it, we've got to use the equation E equal F per Q, where Q is the charge of an electron, just stated, and E is the given stated quantity of 2.5 times 10 to the 4th Newtons per Coulomb. So if I rearrange that equation so as to solve for force, I would have F equal E times Q, and I can multiply my E by my Q and I'll get the force acting upon the electron. Turns out to be exactly 4.0 times 10 to the negative 15th Newtons, which is a very, very small force if you think about it, on the order of 10 times 10 to the negative 15th Newtons. Now force, of course, is relative, so what might be a small force to you could be a huge force to an object that has a mass of 9.11 times 10 to the negative 31st kilograms. In order to determine the acceleration of this object, what we need to do is use Newton's second law equation, A equal F over M, where the M is the mass of the electron, and the F is the electric force that acts upon it. So when you take this really tiny force and divide it by the even more tiny mass to get the acceleration, you get a whopping 4.3908 times 10 to the 15th meters per second per second, and this is the acceleration of that electron.