23.2
Calculation of Electric Flux
Consider the electric field of an oppositely charged, parallel-plate system and an imaginary box between those plates. Let the bottom face of the box…
Consider an imaginary sphere enclosing a positive charge. The electric field due to this charge is directed away from it. The flux points outward on the surface. The opposite occurs if the charge enclosed is negative.
If the charge inside the sphere is increased, the electric field magnitude increases, increasing the electric flux through the surface.
If there is no net charge inside the surface, then the electric field entering equals the field leaving the sphere, resulting in zero electric flux.
Suppose a 1m radius sphere encloses a positive charge of 10 μC. Then, what is the electric flux passing through the sphere?
Using the expressions for the surface area of a sphere and the electric field due to the point charge, the area and electric field magnitude are determined.
Here, the electric field lines are parallel to the area vector, and the angle between these two vectors is zero. By substituting the obtained quantities in the expression for electric flux, the electric flux due to the charge can be calculated.
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Q1: How does the direction of an electric field affect flux through a closed surface?
Electric flux depends on the angle between the electric field and the surface's normal vector. When field lines are parallel to the normal, flux is maximum and positive. When perpendicular, flux is zero. For a positive charge enclosed in a sphere, field lines point outward, creating positive flux. For a negative charge, field lines point inward, creating negative flux.
Q2: Why is the net electric flux zero when no charge is enclosed?
When no charge exists inside a closed surface, every electric field line entering the surface must exit somewhere else. The negative flux entering equals the positive flux leaving, resulting in zero net flux. This occurs because electric field sources lie outside the enclosed volume, so field lines cannot terminate inside.
Q3: What happens to electric flux when the enclosed charge increases?
Increasing the enclosed charge increases the electric field magnitude, which directly increases electric flux through the surface. For example, a 1-meter radius sphere enclosing a 10 microcoulomb positive charge produces greater flux than one enclosing a smaller charge, since flux is proportional to the enclosed charge.
Q4: How do you calculate electric flux through a spherical surface?
Electric flux is calculated using the dot product of the electric field and surface area vector. For a sphere with parallel field lines and area vector, the angle between them is zero. Multiply the electric field magnitude by the sphere's surface area and the cosine of the angle to find the total flux passing through.
Q5: What is the relationship between electric flux and field line direction in a parallel plate system?
In a uniform field between parallel conducting plates, flux through the bottom face is negative because the field opposes the normal vector. Flux through the top face is positive as field and normal align. Flux through side faces is zero since the field is perpendicular to their normals, resulting in zero net flux.
Q6: Why does electric flux cancel out in a box with no enclosed charge?
Flux cancels because electric field sources exist outside the box. Field lines entering the box must exit through another face since no charge inside terminates them. The inward flux through one face equals the outward flux through another, producing zero net flux through the entire closed surface.
Q7: How does charge sign affect the direction of electric flux?
A positive enclosed charge produces outward-pointing electric field lines and positive flux through the surface. A negative enclosed charge produces inward-pointing field lines and negative flux. The sign of flux directly reflects the sign of the enclosed charge, making flux a useful indicator of charge presence.