Calculate the electric field strength inside and outside a wire

In summary, we need to determine the electric field strength inside and outside an infinitely long conducting cylinder of radius R with a uniform surface charge of lambda per unit length. To find the field inside, we can use the equation integral (E.ds) = q/e0 and substitute the charge enclosed by a Gaussian surface inside the conductor. This will result in an electric field strength of zero. To find the field outside, we can use the equation E=q/4(pi)e0R^2 and consider the area of a Gaussian surface, which would be 2(pi)rh + 2(pi)r^2.
  • #1
matt_crouch
161
1

Homework Statement



An infinitly long conducting cylinder of Radius R carries a inform surface charge of (lambda per unit length) determine the electric field strength inside and outside the cylinder

Homework Equations



integral (E.ds)= q/e0

The Attempt at a Solution



im not really sure what to do at all i tried simply differentiating the equation above and substituting lambda in for q but I am pretty sure that's not right...
 
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  • #2
First, the field inside is easiest to start with. The q in integral (E.ds) = q/e0, is the charge inside a gaussian surface. So a gaussian surface inside the conductor encloses how much charge? ... so the electric field is...?

Next, you need to simply integrate the left side of the equation after subtituting dr for ds. Then use a gaussian surface of some length l, and figure out what the q enclosed is and plug that into the right side.
 
  • #3
so since its a Gaussian surface do i calculate the line charge density by integrating lambda from R to infinity? then substitute that into the equation above?
 
  • #4
Electric field inside the cylinder is zero. Because that is conductor material
 
  • #5
ok so outside the conductor do i just use the E=q/4(pi)e0R^2 ?
 
  • #6
matt_crouch said:
so outside the conductor do i just use the E=q/4(pi)e0R^2 ?
It's not correct. What is area of Gaussian surface?
 
  • #7
ahhh so i need to use the area of a cylinder? so 2(pi)rh +2(pi)r^2 ?
 

1. What is the formula for calculating the electric field strength inside a wire?

The formula for calculating the electric field strength inside a wire is E = V/d, where E is the electric field strength, V is the voltage, and d is the distance between two points on the wire.

2. How do you calculate the electric field strength outside a wire?

The formula for calculating the electric field strength outside a wire is E = kq/r^2, where E is the electric field strength, k is the Coulomb's constant, q is the charge of the wire, and r is the distance from the wire.

3. What factors affect the electric field strength inside a wire?

The electric field strength inside a wire is affected by the voltage applied to the wire, the distance between two points on the wire, and the material of the wire. The electric field strength is directly proportional to the voltage and inversely proportional to the distance.

4. How does the electric field strength inside a wire change if the wire is made of a different material?

The electric field strength inside a wire is affected by the material of the wire. Different materials have different electrical properties, such as conductivity and resistivity, which can affect the flow of electric charge and thus the electric field strength. A wire with higher conductivity will have a higher electric field strength compared to a wire with lower conductivity.

5. Can the electric field strength inside a wire be negative?

Yes, the electric field strength inside a wire can be negative. This indicates that the direction of the electric field is opposite to the direction of the voltage applied to the wire. However, the magnitude of the electric field strength is always positive.

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