Calculating Potential Difference in a Uniform Electric Field

[aliaze1]

Homework Statement

What is the potential difference between y_i= -5cm and y_f=5cm in the uniform electric field E = ( 20,000{ i } - 50,000 { j } )V/m?

Homework Equations

∆V = V(s_f) - V(s_i) = -∫ E_s ds

with the limits of the integral being s_f and s_i

The Attempt at a Solution

I tried doing the integral, resulting in (E²)/2, and then multiplying proceding as so:

E= √ (20000² + 50000²) = 53851.64807
(E²)/2 = 14500000 = x
x |_0.05,-0.05 = -{x(0.05) - x(-0.05)} = -{2[x(0.05)]} = -1450000 = incorrect

any help?

thanks!

 

[Anadyne]

I think you're taking the integral as if it were E dE instead of ds (Compare with the case where if it were the integral of x dx, then the integral is x^2/2). E is a constant since it is "uniform", so you can treat it as a constant and pull it out of the integral. If you're only dealing with one dimension (along y), then the integral of E ds simplifies to E(Sf - Si).

 

[aliaze1]

I think you're taking the integral as if it were E dE instead of ds (Compare with the case where if it were the integral of x dx, then the integral is x^2/2). E is a constant since it is "uniform", so you can treat it as a constant and pull it out of the integral. If you're only dealing with one dimension (along y), then the integral of E ds simplifies to E(Sf - Si).

aaahh lol nice...yea that was my mistake...lol whenever i see the integral sign i jump to conclusions without looking at the second part

thanks!

 

[aliaze1]

well actually...i tried that and it didn't work:

E = 53851.64807

S_f-S_i = 0.05 - (-0.05) = 0.1

E * (S_f-S_i) = 53851.64807 * 0.1 = 5385.164807 = Incorrect :(

Any help?

Thanks!

 

[aliaze1]

I have only one attempt left. I noticed that I didn't put the negative sign there, but the computer would tell me to 'check your signs' if this was a sign issue...so i assume it isn't

 

[aliaze1]

any help?