Homework Help: Electric field formula

1. Nov 9, 2015

gracy

1. The problem statement, all variables and given/known data
The electric potential on the surface of a sphere of radius R and charge $3$×$10^-6$ is 500V.The intensity of electric field on the surface of the sphere (in N/C)is

2. Relevant equations
$V$=$(\frac{1}{4πε0}\frac{q}{R})^2$

3. The attempt at a solution
Actually I have solution but still I am unable to understand.So ,instead of my attempt at a solution .I 'll post solution itself.
$V$=$(\frac{1}{4πε0}\frac{q}{R})^2$
$E$=$\frac{\left(\frac{1}{4πε0}\frac{q}{R}\right)^2}{\frac{q}{4πε0}}$

=$\frac{25×10^4}{27×10^3}$

=$\frac{250}{27}$

I want to how the above formula of E is derived.

2. Nov 9, 2015

BvU

Where did you get these squares ? See here

3. Nov 9, 2015

gracy

I didn't get you.

4. Nov 9, 2015

5. Nov 9, 2015

gracy

An image with red cross on it!

6. Nov 9, 2015

BvU

Yeah, company politics forbid easy cut & paste. I uploaded the picture from the link. Which of course you studied extensively ...

7. Nov 9, 2015

gracy

You,king of sarcasm!

8. Nov 9, 2015

gracy

But actually I have studied it extensively before posting this thread(hyperphysics: this site is quite popular after wiki I usually refer this for physics along with physics classroom) ,but could not figure out/extract anything useful from it as you did!

9. Nov 9, 2015

gracy

I am still confused ,please give me a hint !

10. Nov 9, 2015

SammyS

Staff Emeritus
Where did you get the square (as in the exponent being 2) in the above and in the following formulas?

11. Nov 9, 2015

gracy

It has been given in the solution.

12. Nov 9, 2015

BvU

I don't see no solution.

13. Nov 9, 2015

ehild

Gracy, the equation for the potential is wrong. You either copied it incorrectly or your book is wrong. You should know the potential formula for a charged sphere.

14. Nov 10, 2015

gracy

I copied it incorrectly.I know $V$=$\frac{1}{4πε0r}$ It was just by mistake.But I want to know about formula of E

15. Nov 10, 2015

BvU

And what is it you want to know ?

16. Nov 10, 2015

gracy

17. Nov 10, 2015

gracy

I want to make sure there is square in the formula of E!

18. Nov 10, 2015

BvU

Sure. But by squaring $q\over 4\pi\epsilon_0$ you (or the 'solution writer') grabbed the wrong factor !
Check the dimensions too -- very helpful !

19. Nov 10, 2015

gracy

I don't know what is denominator in the formula of E?

20. Nov 10, 2015

gracy

numerator is $V^2$?

21. Nov 10, 2015

gracy

According to his denominator is charge but how can this $\frac{1}{4πε0}$ be charge?

22. Nov 10, 2015

BvU

Electric field strength is Volt/meter, a.k.a. Newton/Coulomb

23. Nov 10, 2015

gracy

But I am told to express E in Newton/Coulomb

24. Nov 10, 2015

BvU

Yes. One and the same thing. Volts is Joule/Coulomb, Electric field is Newton/Coulomb and sure enough, Joule/meter = Newton !

25. Nov 10, 2015

gracy

Here denominator is coulomb means in formula there should be charge as denominator,right?