Why does electric flux have 'cos θ' in its formula?

[AnandM]

Why does electric flux have 'cos θ' in its formula??

 

[Doc Al]

Why does electric flux have 'cos θ' in its formula??

To find the flux through a surface you need the component of the field perpendicular to the surface. Taking that component involves the cosine of the angle between the field and the normal to the surface.

Read about it here: Electric Flux

 

[AnandM]

Why does it have to ve perpendicular? Why not at any other angle?

 

[Doc Al]

Why does it have to ve perpendicular? Why not at any other angle?

If you want to maximize the flux through a surface, you want to orient the surface so that its normal is parallel to the field.

As an analogy, think of rain falling straight down (representing the field). You have a bucket that you want to fill quickly. How would you orient the open surface of the bucket to maximize the amount of rain collected? Obviously, you'd arrange the bucket upright so that the "flux" is maximum. That would have the normal to the surface (which is used to describe the orientation of the surface) parallel to the falling rain. That makes the angle θ = 0, making cosθ = 1. If you turned the bucket sideways so that θ = 90°, cosθ = 0 and the flux goes to zero. (The bucket won't fill up at all.)

 

[AnandM]

So are we using cos θ because the sin θ component gives 0 flux?

 

[Doc Al]

So are we using cos θ because the sin θ component gives 0 flux?

You use cos θ because you want the component of the field in the direction of the surface normal. Whenever you need a component of a vector in a certain direction, you multiply the magnitude of the vector by the cosine of the angle it makes with that direction.

For example, to find the x-component of a velocity vector ($\vec {V}$), you use $V\cos\theta$, where $\theta$ is the angle the vector makes with the x-axis.

 

[AnandM]

Okay thanks