How Is Electric Potential Calculated Between Two Points in a Field?

[Strawer]

Homework Statement

An electric field is given by E = 2xi-3y²j N/C. Find the change in potential from the position r_A = i - 2j m to r_B = 2i + i + 3k m.

Homework Equations

V_B - V_A = -$\int_A^B$ E$\cdot$ds

The Attempt at a Solution

ΔV= -$\int_1^2$2x dx - $\int$-3y^2 dy

The second integral is supposed to be from -2 to 1

And when I calculate this I get -10 V when the answer is +6 V

I also noticed that if I simply invert the limits on the integral I get +6 V, is it just a coincidence or have I calculated the integral wrong?

 

[ehild]

You can have a sign error somewhere. Show your work. ehild

 

[Strawer]

Well i have noticed that I'm very prone to making rudimentary mistakes often but I don't believe that to be the case here.

When calculating the integral I do as follows:

- $\left[ x^2 \right]_{1}^{2}$ - $\left[ -y^3 \right]_{-2}^{1}$ =
-(4-1) - (-1+8)= -3 - 7 = -10 V

 

[ehild]

You made the sign error at y^3. At the lower bound it is -(-(-(-8)))

-x^2-(-y^3)=-x^2+y^3.


-(4-1)+(1^3-(-2)^3)=-3+(1+8)=6

ehild

 

[Strawer]

You made the sign error at y^3. At the lower bound it is -(-(-(-8)))

-x^2-(-y^3)=-x^2+y^3.


-(4-1)+(1^3-(-2)^3)=-3+(1+8)=6

ehild

Oh I see now. My homework would be a lot loss painful if I could avoid stuff like this but it doesn't matter how thorough I am, I often miss things anyways. I think I might have a mild form of dyscalculia or something..

But thank you for your assistance!

 

[ehild]

Get rid of the lot of minuses as soon as possible and use parentheses. No dyscalculia. I got the correct result at the fourth attempt.

 

[Strawer]

Get rid of the lot of minuses as soon as possible and use parentheses. No dyscalculia. I got the correct result at the fourth attempt.

Hehe well it's good to know that I'm not the only one who struggles with stuff like that

 

[SammyS]

What is the z coordinate for r_A ?

 

[Strawer]

What is the z coordinate for r_A ?

There isn't a z coordinate for r_A but as I understand that doesn't matter anyways since the electric field has no component in the z direction.

 

[ehild]

There isn't a z coordinate for r_A but as I understand that doesn't matter anyways since the electric field has no component in the z direction.

That is the z coordinate is 0.

ehild

 

[SammyS]

That is the z coordinate is 0.

ehild

Yup , so r_B - r_A has a z component.

 

[ehild]

It has, but E has not.

ehild