Two equipotential surfaces are shown. If Va = -5V and Vb = -15V, find the work needed to move a -2μC charge from A to B along the indicated path.
- First of all, does the path of the charge going from A to B matter or can I just calculate using the "distance" variable (when or if needed) to be the straightest line between A and B? And then how would I continue from here?
This is a problem about POTENTIAL!
The path does not matter ! That is the whole point.
The voltage potential difference is the difference in potential energy of a unit charge at the two voltages.
work done = charge * change in V
Alrighty, thank you!
The path of the charge going from A to B does matter because the work done in moving a charge depends on the electric field along the path. The work done (W) in moving a charge (q) from one point to another can be calculated using the equation:
W = q * ΔV
Where ΔV represents the change in electric potential between the two points (in this case, between points A and B).
To determine the work needed to move the charge from A to B along the indicated path, you need to find the change in electric potential (ΔV) between these points.
Since the electric potential is a scalar quantity, it is constant along an equipotential surface. Therefore, the work done along the path depends solely on the potential difference between the equipotential surfaces that contain points A and B.
Given that Va = -5V and Vb = -15V, the change in electric potential (ΔV) between A and B can be calculated as follows:
ΔV = Vb - Va
= -15V - (-5V)
= -15V + 5V
= -10V
Now that you have determined the change in electric potential (ΔV), you can proceed to calculate the work done to move the charge from A to B.
The next step is to determine the charge (q) that is being moved. In this case, it is -2μC (microcoulombs) as mentioned.
Finally, you can calculate the work (W) needed to move the charge from A to B as follows:
W = q * ΔV
= (-2μC) * (-10V)
Remember to convert -2μC to coulombs before the calculation. 1μC is equal to 10^-6C.
So, you have the work (W) needed to move the charge from A to B along the indicated path.