Consider the movement of 1C of positive charge in a uniform electric field as shown below.
(Just a diagram of a plate with the positive plate at the top, and a positive charge placed in the field at the top, and then moving towards the bottom. No numerical values given for d, or v; they're just labelled as the letters).
The question states: Compare the kinetic energy of the Coulomb of charge at the top plate to the kinetic energy of the charge right before it collides with the bottom plate.
Halllp. How do you find the kinetic energy in terms of electricity?
Hey! I don't think you'd need to quantify any relationship. You'd rather need to discuss, generally, what the hell is going on.
In an electric field, a charged particle experiences a force. That force is the same, no matter where in the electric field you are, assuming that the electric field stays constant (which it does here). So, what can we say about the force?
There is a constant force pushing the charge downwards!Does that sound familiar? Well, it should; that's how gravity works as well! If there is a constant force applied, in the same direction, then the particle will
accelerate downwards. So, if you just wanted to qualitatively discuss the kinetic energy, you'd say that it starts off at zero (as it is at rest), and then increases and an increasing rate the further down it is 'pushed'.
However, you could get a bit more technical than that. You could find that constant accelerating force, and label it 'a'. Then, you could literally just apply the same formulas that you use for projectile motion! For instance, we know that
However, the initial velocity is zero (assuming the particle at rest). So, the velocity of the particle will always be the accelerating force 'a', multiplied by time. Thus, we can plug this into our kinetic energy formula
^2)
None of this last part is necessary, just interesting the think about
Edit: A bit more 'precise'We actually know that the force on a charged particle is
Here, q is equal to 1 C, so
But, force also equals mass times acceleration, so
Putting this into our kinetic energy formula
^2)
If I'm honest, we could also figure out a better value than t, using the known distance between the plates. ie. We could find how long it takes the particle to cover a distance, d, using projectile motion formulas. All of this is probably beyond the question, so I'll stop here.
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