Physics question help please!

[holdmystethoscope]

Hello all, I am confused between two formula First one is v=k(q/r) which says the voltage increases as distance (r) decreases. Later I found another formula of voltage which says v=Ed (where d is distance and voltage increases as distance increases). Seems contradictory. Will you please let me know how these two situations are different? Also what the heck is a point charge? Thank you so much for your time.

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[yeezuswest]

I think the difference is that the second one (which should be deltaV=-Ed) is more conceptual and is referring to "deltaV" (potential difference), which simply says that the electric field E will point in the direction of decreasing potential over a distance d. You always want to go from an area of high potential energy to an area of low potential energy.

The other equation (V=kq/r) is referring to just "V" and gives you a measure of electric potential (in volts) for a point change Q.

 

[jjmusicman29]

They're the same principles expressed through two different but exactly related formulas.

I'll try my best to explain by recalling these formulas from memory. Sorry if I make an algebra or assumption mistake.

I'm going to ignore calculus for this explanation, so these formulas are very basic because they don't incorporate vectors or direction.

First start with this.

The total electrostatic force caused by a single charge (q1) upon another charge (q2) is governed by this classic formula:

F = k(q1)(q2)/r^2

where k is a physical constant, r is the distance between the two charges, and it is assumed these two charges lie on the x- or y-axis to simplify trigonometry/vectors.

The electric field intensity that (q2) experiences due to the charges around it (in this case, just q1) is

E = k(q1)/r^2

The (q2) is missing from this formula because you're only interested in the electric field caused by the surrounding charges in an area on a single point (q2). You are not interested in the magnitude of (q2)'s charge, or therefore the total resulting force upon a single point (q2), which would have to incorporate (q2) in the formula because total force is a sum of all forces (Newton's Laws).

Let's simplify this formula by calling (q1) just q.

E = k(q/r^2)

Now, voltage (V) is a potential energy difference. An energy or work is a force times a path that the force travels. Ie, energy = force*distance if the path is an easy, straight line. If you work out the calculus, the potential energy difference will be V = E*d.

Voltage is the work that happens from the electric field working over a distance. Conceptually, voltage is like the work provided by ocean waves (electric field caused by surrounding charges) pushing you a distance against the shore.

V = E*d.

In our example, the distance (d) is actually r.

So V= (k(q/r^2))*r = k(q/r)

V = k(q/r)

This means as the distance increases, the voltage increases because voltage is a potential energy difference, so the difference in potential energy between the start of the electric field and where it is being experienced increases as the distance increases.

 

[laballsummer]

E in your second formula is for Electric field, the formula for which is:

E = k(Q/R^2)

By multiplying E by D, we get your first equation. They're just different equations that describe the same thing.