Welcome to the PF.momowoo said:So in a graph where V is a function of x, when the slope is negative what does that mean about the direction of the field along the x axis? What about when the slope is positive?
That's not what I'm picturing, but perhaps it might work as well. But it would take multiple hollow concentric conducting spheres charged to different voltages, no?momowoo said:
Exactly. So what does that tell you about your diagram?momowoo said:
Where the graph shows a positive slope, the positive test charge would tend to move towards lower potential (to the left). So what direction must the field be in that region?momowoo said:
Just specify the direction with respect to the x-axis given. ("To the right" corresponds to the +x direction, in this case.)momowoo said:
Yes. Where the potential rises to the right, the field points left.momowoo said:
Yes. The field is related to the negative (opposite) of the slope of the potential graph. So where the slope is positive, the field is negative -- pointing to the -x axis (to the left, in this case). And where the slope is negative, the field is positive.momowoo said:
You are very welcome.momowoo said:
Electric potential refers to the amount of electric potential energy per unit charge at a given point in an electric field. It is a measure of the electric potential energy a charged object would possess at a specific point in the electric field.
While electric field measures the force exerted on a charged object at a specific point in the electric field, electric potential measures the potential energy that the charged object would possess at that same point. Electric potential is therefore a scalar quantity, while electric field is a vector quantity.
The unit of electric potential is volts (V), which is equivalent to joules per coulomb (J/C).
Electric potential is calculated using the formula V = kQ/r, where V is the electric potential in volts, k is Coulomb's constant (8.99 x 10^9 Nm^2/C^2), Q is the charge of the object in coulombs, and r is the distance from the object in meters.
Electric potential energy is the energy a charged object possesses due to its position in an electric field. It is directly proportional to the electric potential, with the equation U = qV, where U is the electric potential energy in joules, q is the charge of the object in coulombs, and V is the electric potential in volts.