How do I compute electric flux through a half-cylinder

In summary, the problem involves finding the flux through a half-cylinder with given dimensions and a known magnitude of electric field. The student first attempted to use the equation flux = E * A, but it did not work. They then tried finding the area of the rectangular side of the half-cylinder, but that also did not work. The student is unsure if a different equation should be used and if they need to specify the units of the final result.
  • #1
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Homework Statement


In figure 1, take the half-cylinder's radius and length to be 3.4cm and 15cm respectively.
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If the electric field has magnitude 5.9 kN/C, find the flux through the half-cylinder. Hint: You don't need to do an integral! Why not?

Homework Equations

The Attempt at a Solution


I tried finding the area of the cylindrical surface and multiplying that by the magnitude of the electric field. That didn't work. Then I tried finding the area of the rectangle that would be the further side of the half-cylinder and multiplying that by the electric field but again, that didn't work.

Do I need to use a different equation? I was originally using flux = E * A. Should I be using something else?
 
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  • #2
Can you show the details of your calculation for the rectangular area method? E*A should work. Are you supposed to specify the result in particular units?
 

FAQ: How do I compute electric flux through a half-cylinder

1. What is the formula for computing electric flux through a half-cylinder?

The formula for computing electric flux through a half-cylinder is Φ = ε₀EcosθA, where Φ represents the electric flux, ε₀ is the permittivity of free space, E is the electric field strength, θ is the angle between the electric field and the surface of the half-cylinder, and A is the area of the curved surface.

2. How do I determine the direction of the electric field for computing electric flux through a half-cylinder?

The direction of the electric field is perpendicular to the surface of the half-cylinder, pointing either towards or away from the curved surface depending on the direction of the electric field. This can be determined using the right-hand rule, where your fingers point in the direction of the electric field and your thumb points in the direction of the flux.

3. Can I use Gauss's Law to compute electric flux through a half-cylinder?

Yes, Gauss's Law can be used to compute electric flux through a half-cylinder. It states that the electric flux through a closed surface is equal to the charge enclosed by that surface divided by the permittivity of free space. This can be applied to a half-cylinder by considering the curved surface as the closed surface and the charge enclosed as the charge on one half of the cylinder.

4. How do I determine the area of the curved surface for computing electric flux through a half-cylinder?

The area of the curved surface of a half-cylinder can be calculated using the formula A = 2πrh, where r is the radius of the cylinder and h is the height of the cylinder.

5. Can I compute electric flux through a half-cylinder if the electric field is not constant?

Yes, electric flux can still be computed through a half-cylinder if the electric field is not constant. In this case, the electric field strength and direction must be known for each point on the curved surface, and the flux can be calculated by integrating the electric field over the area of the curved surface.

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