Find the enclosed charge

  • #1
174
0

Homework Statement


I'm to find the enclosed charge of the closed surface in the image (not sure how to describe the shape).

The Attempt at a Solution


Let [itex]a=4cm[/itex] and [itex]b=5cm[/itex]. The total flux in is then [itex]abE_1[/itex] and flux out is [itex]abE_2[/itex]. Applying Gauss' law then gives the total enclosed charge as [itex]Q=ab\epsilon_0(E_2-E_1)[/itex].

The step I'm a little unsure about is taking the total flux out to be [itex]E_2[/itex] times the area [itex]ab[/itex], since the electric field [itex]E_2[/itex] is through a slanted surface, not perpendicular. On the other hand, the total flux through that slope would have eventually to pass through an area of [itex]ab[/itex]...
 

Attachments

Answers and Replies

  • #2
gneill
Mentor
20,909
2,858

Homework Statement


I'm to find the enclosed charge of the closed surface in the image (not sure how to describe the shape).

The Attempt at a Solution


Let [itex]a=4cm[/itex] and [itex]b=5cm[/itex]. The total flux in is then [itex]abE_1[/itex] and flux out is [itex]abE_2[/itex]. Applying Gauss' law then gives the total enclosed charge as [itex]Q=ab\epsilon_0(E_2-E_1)[/itex].

The step I'm a little unsure about is taking the total flux out to be [itex]E_2[/itex] times the area [itex]ab[/itex], since the electric field [itex]E_2[/itex] is through a slanted surface, not perpendicular. On the other hand, the total flux through that slope would have eventually to pass through an area of [itex]ab[/itex]...
The area [itex]ab[/itex] is correct. You want to sum the component of the flux which is normal to the surface it passes through. If you do the geometry you'll find that for a flat surface at an angle to the flux, this amounts to the cross sectional area which is perpendicular to the field vectors.
 

Related Threads on Find the enclosed charge

  • Last Post
Replies
6
Views
404
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
11
Views
13K
  • Last Post
Replies
5
Views
11K
Replies
2
Views
2K
Replies
1
Views
3K
Replies
1
Views
896
Replies
3
Views
2K
Replies
1
Views
2K
Replies
5
Views
9K
Top