Work required to move charge

In summary, the conversation discusses the work required to bring a charge from infinity to a corner of an equilateral triangle with two other charges at the other corners. The solution involves calculating the voltage at the point and using it to find the work using the formula q*ΔV. The final result is q2 / 2*pi*epsilon*a.
  • #1
indie452
124
0

Homework Statement



situation:
there are two charges (+q) one at one corner of an equilateral triangle the other at another corner. the triangle has sides length a.

what is the work required to bring another charge (+q) in from infinity to the other corner on the equilateral triangle.

The Attempt at a Solution



ok so i know dW = -dU = F.dl

i thought that maybe finding (F) at the corner that we are bringing the charge to may help...this is:
Fc [at corner] = q2 / 2*pi*epsilon*a2

then i could just integrate this over the distance i am moving it with respect to a...however i know that the one limit will be [tex]\infty[/tex] however i don't know what the other will be

thanks for any help
 
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  • #2
Consider the Voltage at the point from each of the 2 other charges.

V = k*q / r

Since work = q*ΔV

and V = 0

Then

Work = q*ΣV
 
  • #3
ok so
the E at the point is 2q / 4*pi*epsilon*a2
the V at the point is 2q / 4*pi*epsilon*a

so work to bring in point is = q(2q / 4*pi*epsilon*a) = q2 / 2*pi*epsilon*a
 
  • #4
indie452 said:
ok so
the E at the point is 2q / 4*pi*epsilon*a2
the V at the point is 2q / 4*pi*epsilon*a

so work to bring in point is = q(2q / 4*pi*epsilon*a) = q2 / 2*pi*epsilon*a

Looks like it.

Though E is a vector, don't forget, and V is a scalar here. In your first equation then the E would need to be added as vectors. Whereas for V you are adding scalars.

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/mulpoi.html#c1
 
  • #5
ok thanks...:biggrin:
 

What is "Work required to move charge"?

The work required to move charge refers to the amount of energy needed to move an electric charge from one point to another. This is known as electrical work and is measured in joules (J).

How is the work required to move charge calculated?

The work required to move charge is calculated by multiplying the magnitude of the charge (in coulombs) by the change in electric potential (in volts) between the two points. This can be represented by the equation W=qΔV, where W is work, q is charge, and ΔV is change in electric potential.

What is the relationship between work required to move charge and distance?

The work required to move charge is directly proportional to the distance between the two points. This means that as the distance increases, the work required to move the charge also increases. This relationship is known as Coulomb's Law and is represented by the equation W=1/4πε0q1q2/r, where ε0 is the permittivity of free space, q1 and q2 are the two charges, and r is the distance between them.

What factors affect the work required to move charge?

The work required to move charge is affected by the magnitude of the charge, the distance between the two points, and the presence of any other charges in the surrounding area. It is also affected by the medium through which the charge is being moved, as different materials have different electrical properties that can impact the work required.

Why is understanding the work required to move charge important?

Understanding the work required to move charge is important in many applications, such as designing electrical circuits, calculating the efficiency of electrical devices, and understanding the behavior of electric fields. It is also crucial in the development of new technologies and advancements in the field of electricity and magnetism.

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