potential difference=40v b2n plate A & B.
find work done if q=+3C from
a) B to A
b) A to B
*i already know the ans but i need the explanation for the formula.
-this is my work
a)w=-qv b)-120J
=-3(-40)
=120 J
what i want to ask is:
1-why must we add - sign for v is not that if the v is against electric field is +?
You don't say whether A or B has the higher potential. You only say that the difference "between" them is 40 V.
If a positive charge moves to a higher potential, the potential energy increases. The E field and force is opposite to the direction of motion in that situation.
i'm sorry. the electric field are from A to B.
dear drwls,you didn't answer my question.
i know about the concept but why the v is negative? or how can it be proven mathematically by the formula?.
Start with the definition of work
Work=Force dot distance
= Eq dot distance
but E=-dV/dx by definition of direction of E field. E goes from + V to -V (the direction of a pos test charge)
Work= q*-dV/dx dot distance
work= -q dV/dx dot dx
Now, if the distance is in the direction of the gradient, then
work=-q DeltaV
To understand why we add a negative sign in the formula for work done (w = - qV), let's break down the equation and consider the concepts involved.
Work done, w, is given by the equation w = Fd, where F is the force applied and d is the displacement. In the context of electric fields, the force experienced by a charged particle is given by F = qE, where q is the charge of the particle and E is the strength of the electric field.
The potential difference, V, between two points in an electric field represents the difference in electric potential energy per unit charge. It is measured in volts (V). Mathematically, potential difference is given by V = Ed, where E is the electric field strength and d is the distance (or displacement) between the two points.
Now, let's consider the direction of the electric field. Electric fields always point from positive charge to negative charge. If we have a positive charge (q > 0) that moves in the direction of the electric field, then the force experienced by the charge and the displacement will be in the same direction. In this case, both q and d are positive, so the work done will be positive.
However, if the charge moves against the electric field (from a region of higher potential towards a region of lower potential), the force and displacement will be in opposite directions. In this case, q will still be positive, but d will be negative because the displacement is opposite to the direction of the electric field. Thus, when calculating the work done, we need to account for this by including the negative sign.
Therefore, to calculate the work done when moving a positive charge from point B to A (against the electric field), we use the formula w = -qV. The negative sign indicates that work is done against the field. Similarly, when moving the charge from A to B (along the electric field), no additional negative sign is required, as the displacement and electric field direction are aligned, resulting in positive work done.