# 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 $V^2$?