Two charges of 1.0 μC and -2.0 μC are 0.50 m apart at two vertices of an equilateral triangle a

Two charges of 1.0 μC and -2.0 μC are 0.50 m apart at two...

Two charges of $1.0 \mu \mathrm{C}$ and $-2.0 \mu \mathrm{C}$ are $0.50 \mathrm{~m}$ apart at two vertices of an equilateral triangle as in Figure $\mathrm{P} 16.60 .$ (a) What is the electric potential due to the $1.0-\mu \mathrm{C}$ charge at the third vertex, point $P ?$ (b) What is the electric potential due to the $-2.0-\mu \mathrm{C}$ charge at $P ?$ (c) Find the total electric potential at $P$. (d) What is the work required to move a $3.0-\mu \mathrm{C}$ charge from infinity to $P$.

Two charges of $1.0 \mu \mathrm{C}$ and $-2.0 \mu \mathrm{C}$ are $0.50 \mathrm{~m}$ apart at two vertices of an equilateral triangle as in Figure $\mathrm{P} 16.60 .$
(a) What is the electric potential due to the $1.0-\mu \mathrm{C}$ charge at the third vertex, point $P ?$ (b) What is the electric potential due to the $-2.0-\mu \mathrm{C}$ charge at $P ?$ (c) Find the total electric potential at $P$. (d) What is the work required to move a $3.0-\mu \mathrm{C}$ charge from infinity to $P$.

Key Concepts

Work and Electric Potential Energy

Work in the context of electrostatics relates to the energy required to move a charge within an electric field. Specifically, the work done in moving a charge from one point to another is equal to the change in electric potential energy, which can be computed using the relation W = q?V, where q is the test charge and ?V is the electric potential difference between the points.

Electric Potential of a Point Charge

This concept describes the amount of electric potential energy per unit charge created by a point charge. It is given by the formula V = kq/r, where k is Coulomb's constant, q is the charge, and r is the distance from the charge. The potential is a scalar quantity, which makes it easier to calculate the total potential from multiple charges by simple algebraic addition.

Superposition Principle in Electrostatics

The superposition principle states that the total electric potential at a point due to several charges is the algebraic sum of the potentials due to each individual charge. This principle holds because electric potential is a scalar quantity, allowing for straightforward addition without needing to consider vector components.

Transcript

00:01 As an example of potential and potential energy for point charges, we are going to figure out the work it will take to drop a positive charge at point p, which is the top vertex in an equilateral triangle.

00:19 And along the bottom are two charges at the vertices.

00:24 There's a positive one micro, which is 10 to the minus 6, coulums, on the left and a negative 2 microculems on the right.

00:37 So the first goal is to find the potential at point p using the potential formula for point charges.

00:47 It's the electrical constant k times charge q over the distance from that charge.

00:55 So we can find the potential at point p due to the positive one microculum.

01:04 K is just 9 times 10 to the 9th in si units.

01:12 And we have one microculum.

01:17 And our separation is given to us as 0 .5 meters.

01:26 So not surprisingly, that's a positive potential.

01:33 And we can do the same for the negative charge.

01:50 And so that's a fairly straightforward.

01:52 It's not surprisingly a negative potential.

02:01 What we know about electric potential is that it just adds.

02:07 So we can find the total potential at point p by just simply adding those two together.

02:18 And if there were many other different charges, we could add them in as well.

02:23 But we get minus 1 .8 times 10 to the 4 volts.

02:32 Now for the work.

02:34 The work done by an external agent, not the field, but an external agent, is going to be positive change in potential energy, which is q times delta v.

02:51 The reminder that what a delta is is a final minus initial...

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