Two wires in parallel and capacitence

In summary, the problem is to find the capacitance per unit length for two identical wires separated at a distance D with a given formula. The approach involves using the formula C = q / V and considering the charge distribution on the wires. By calculating the potential difference between the wires using the formula phi = 2 lambda ln(r/d) and then using this to calculate C/l = lambda/V, the capacitance per unit length can be determined.
  • #1
mattysimins
4
0
I have to show that the capacitance per unit length for two identical wires of radius d separated (at the center) a distance D as:

C/l = (pi epsilon0) / ( ln [( D - d ) / d]

And I'm clueless. How do I go about solving this?

I started by trying with C = q / V to C = lambda * l / V .. but I didn't get far as I didn't know what to do with lambda.

Edit: they are oppositely charged, and the charge is distributed evenly along the surface of each wire.
 
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  • #2
Calculate the potential difference V between the two wires
using phi=2\lambda ln(r/d) (in Gaussian units) for each wire.
Then C/l=\lambda/V
 

What is the definition of capacitance?

Capacitance is the ability of a system to store an electric charge. It is measured in Farads (F) and is determined by the geometry and material properties of the system.

How do two wires in parallel affect capacitance?

When two wires are placed in parallel, the overall capacitance increases. This is because the total surface area of the system increases, allowing for more charge to be stored.

What is the equation for calculating the total capacitance of two wires in parallel?

The equation for calculating the total capacitance of two wires in parallel is C = C1 + C2, where C1 and C2 are the individual capacitances of the two wires.

How does the distance between the two wires affect capacitance?

The distance between the two wires has an inverse relationship with capacitance. As the distance increases, the capacitance decreases. This is because the electric field between the wires weakens, reducing the ability to store charge.

What are some real-life applications of two wires in parallel and capacitance?

Two wires in parallel and capacitance are commonly used in electronic circuits, such as in capacitors and power lines. They are also used in communication devices, such as coaxial cables and antennas, to improve signal strength and reduce interference.

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