Ranking E field in equipotential surfaces, confused

In summary, the conversation discusses the concept of equipotential surfaces and their relationship to the electric field. The question at hand is regarding the ranking of three different arrangements of equipotential surfaces based on the magnitude of the electric field present. The conversation also touches on the direction of the electric field and the calculation of its magnitude using the equation E = -dV/dx. The ranking of the arrangements is determined to be 1>2=3 based on the calculations for the electric field in each arrangement.
  • #1
mr_coffee
1,629
1
Hello everyone I'm confused on this topic. I read about it in the book and it made sense though. The question is: Figure 24-25 shows three sets of cross sections of equipotential surfaces; all three cover the same size region of space.
Diagram: http://www.webassign.net/hrw/25_29.gif

(a) Rank the arrangements according to the magnitude of the electric field present in the region, greatest first (use only the symbols > or =, for example 1=2>3).


(b) In which is the electric field directed down the page?


Well in the book it says, E is always perpendicular to the equipotential surfaces and I get that, also i understand that if a charged particle moves from one end to the other but still ends up on the same equipotential surface, the work done is 0. Also if you moved a charged particle to a difference surface, and u moved another charged particle to the same surface, the work done would be equal to each other, because they are both on the same equipotential surface. But for part (a) I'm confused, what equation would I use to calculate the E field, do i assume there is a charged particle moving from each surface to the next until it hits the last one or what? Also for part (b), wouldn't they all be pointing downwards? if i assumed there was a charged particle star4ting at the top of the surfaces, because a + charges E field is always directing away from it, wouldn't they all be down the page?:bugeye:
 
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  • #2
[tex] E = - dV/dX = - \Delta V/ \Delta x [/tex] for unidirectional field, gives that potential decrease in the direction field hence field is upward in 1 and 2 but downward in 3.

for first
[tex] \ E_1 = - (80 -100)/x = 20/x [/tex]
for second
[tex] \ E_2 = - (-120+100)/2x = 20/2x [/tex]
for third
[tex] \ E_3 = - (-30 + 50)/2x = - 20/2x [/tex]
so 1>2=3
 
  • #3



Hello there! It's great that you're trying to understand this topic. Ranking the electric field in equipotential surfaces can be confusing at first, but let me try to break it down for you.

First, let's define what equipotential surfaces are. They are imaginary surfaces in space where the electric potential (V) is constant. This means that if you were to move a charged particle from one point on the surface to another, no work would be done since the potential remains the same.

Now, to rank the arrangements according to the magnitude of the electric field present, we need to think about how the electric field lines are distributed in each diagram. Remember that electric field lines always point perpendicular to equipotential surfaces. So, in arrangement 1, the electric field lines are more concentrated and closer together compared to arrangement 2 and 3. This means that the electric field is stronger in arrangement 1. In arrangement 2, the electric field lines are more spread out, indicating a weaker electric field. In arrangement 3, the electric field lines are almost parallel to each other, showing the weakest electric field.

Therefore, the ranking would be: 1>2>3. This means that arrangement 1 has the strongest electric field, followed by arrangement 2 and then arrangement 3.

For part (b), you are correct in saying that the electric field is directed perpendicular to the equipotential surfaces. However, the direction of the electric field is determined by the sign of the charges present. In this case, we don't know the sign of the charges, so we cannot determine the direction of the electric field. It could be pointing downwards, upwards, or in any other direction.

I hope this helps clarify your confusion. Remember, the key to understanding this topic is to visualize how the electric field lines are distributed in each arrangement. Keep practicing and you'll get the hang of it!
 

1. What are equipotential surfaces?

Equipotential surfaces are imaginary surfaces in a region of space where the electric potential is constant at every point on the surface. This means that no work is required to move a charge between any two points on the surface.

2. How do you rank the electric field in equipotential surfaces?

The electric field is perpendicular to the equipotential surfaces, and its strength can be determined by the spacing between the equipotential surfaces. The closer the spacing, the stronger the electric field.

3. Why is it confusing to rank the electric field in equipotential surfaces?

It can be confusing because the electric field is always perpendicular to the equipotential surfaces, so it may seem like the electric field is the same at every point on the surface. However, the strength of the electric field can vary depending on the spacing of the equipotential surfaces.

4. What is the relationship between electric potential and electric field?

Electric potential is the amount of work required to move a unit positive charge from one point to another in an electric field. The electric field, on the other hand, is the force per unit charge at a given point in space. They are related by the equation E = -∇V, where E is the electric field, V is the electric potential, and ∇ is the gradient operator.

5. How do equipotential surfaces relate to electric potential and electric field?

Equipotential surfaces are a visual representation of electric potential. The electric field is always perpendicular to the equipotential surfaces, and the spacing between the surfaces can indicate the strength of the electric field. In other words, equipotential surfaces help us visualize and understand the relationship between electric potential and electric field in a given region of space.

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