# Derivatives in physics

1. Dec 16, 2014

### gracy

Can anyone explain what actually use of derivatives in physics.It's totally beyond my understanding.I was doing gauss law and i came across this derivative doubt.In the video at time 8:13 to 8:33

what he means by saying if area is small electric field should be approximately constant?is he talking about uniform electric field?Or he means all such dA would have same value and direction of electric field?
what he actually meant by constant electric field -
(1)same electric field for all dA OR
(2)uniform electric field?
which one ( 1)or (2)?

Last edited: Dec 16, 2014
2. Dec 16, 2014

### Staff: Mentor

This is not a derivative. He is considering an infinitely small area dA. To this infinitely small area corresponds an infinitely small flux dΦ. To get the total flux Φ, you need to sum the small fluxes, but since the fluxes are infinitely small, the sum becomes an integral.

I think the explanation given in the video is pretty good for this level. Can you point out more specifically what you don't understand?

3. Dec 16, 2014

### Staff: Mentor

Twice, he said "the electric field is approximately constant over it", it being the small element of area dA. Even if the electric field is varying on the large scale, over a small enough area, it doesn't vary much. That's all he was trying to say.

Chet

4. Dec 16, 2014

### gracy

how electric field vary?what is variation in electric field?does variation in electric field mean electric field is not uniform ?

5. Dec 16, 2014

### Staff: Mentor

It depends on the situation. For example, for a point charge, the magnitude (strength) of the field varies with distance r from the charge: $$E = \frac{q}{4 \pi \epsilon_0 r^2}$$ (Coulomb's Law). The direction of the field varies with location because it's always directly away from a positive charge, or directly towards a negative charge.

6. Dec 16, 2014

### gracy

So how does infinitely small area REDUCES ELECTRIC FIELD VARIATION?

7. Dec 16, 2014

### Staff: Mentor

To make an analogy, the earth is a sphere, so the direction of "up" (away from the center of the earth) varies from one location to another. It's much different in London than in Singapore. :D But if you stay inside London, "up" is very nearly the same everywhere.

Likewise, the strength of the earth's gravitational field varies as 1/r2 where r is the distance from the center of the earth. Nevertheless, in typical laboratory situations near the earth's surface we usually assume it's uniform with height (9.81 m/s2). The difference between floor and ceiling is far too small to bother with.

8. Dec 16, 2014

### gracy

hmmm.........great analogy .So here earth is total area say A.direction of up is electric field.London ,singapore and several other countries would be different dA .

9. Dec 16, 2014

### gracy

But what about integrating all those dA?won't it become A again so again variable electric field at different points?

10. Dec 16, 2014

### gracy

11. Dec 16, 2014

### Staff: Mentor

No. You are integrating over an area, but the integrand of dA is not 1. In the case being considered in the video, the integrand is the component of the field strength normal to dA. So, of course, you don't get A when you integrate, since the component of the field strength normal to dA varies over the surface.

Chet

12. Dec 16, 2014

### gracy

Till dA i understood but why integration is done ?

13. Dec 16, 2014

### gracy

Till dA i understood but why integration is done ?

14. Dec 16, 2014

### Staff: Mentor

In the example on the video, the guy is trying to determine the "electric flux" through a surface. This requires you to do integration over the surface if the normal component of the field strength is varying with position at the surface.

Chet

15. Dec 16, 2014

### gracy

Here is my understanding.We want flux i.e lines of electric field E linked with an area A.So flux is proportional to area as well as electric field.So we can multiply electric field in unit area ( if it is same throughout the area)) and multiply it by area A.But what if electric field is not uniform?So for this we take extremely small area dA and being so small electric field here is constant (does not vary) and we will take what is electric field in this dA .Then we multiply this electric field( electric field in dA)with integral (i.e adding up all such dA)to get total flux.
Where i am wrong?
here i have assumed electric field lines to be straight not at any angle.

16. Dec 16, 2014

### Staff: Mentor

Yes, if you mean by the last sentence that you are describing the special case in which the field lines are perpendicular to the surface at each location on the surface.

17. Dec 16, 2014

### gracy

Is it correct?

18. Dec 16, 2014

### Staff: Mentor

Yes, if the area is planar and normal to the electric field.

19. Dec 16, 2014

### gracy

What integral of dA would be in this case?Total area A ,right?

20. Dec 16, 2014

Sure.

Chet