A charge q =+ 4.11 x 10 - 9 C is placed at the origin, and a second charge equal to -2q is placed on the x axis at the location x = +1.00 m. (a) Find the electric potential midway between the two charges. (b) The electric potential vanishes at some point between the charges. Find this value of x.

Well, it turns out potential is scalar, so you just add. Find where they add to zero.

I don't understand what you're trying to say when you're saying to add. Can you elaborate more?

Vtotal=V1+V2=kq1/x +kq2/x, you know distancex (1/2 of 1), and you know the two q.

when is potential zero> Set Vtotalt to zero, and solve. one distance x, the other 1-x.

You can do that.

Ok that makes much more sense. Thank you for your help!

To find the electric potential at a point, you need to use the formula for electric potential due to a point charge. The formula is given by:

V = k * q / r

Where:
V represents the electric potential,
k represents the electrostatic constant (8.99 x 10^9 N m^2/C^2),
q represents the charge, and
r represents the distance from the charge.

(a) Find the electric potential midway between the two charges:
To find the electric potential halfway between the two charges, you need to find the contributions from both charges and add them together.

Let's denote the charge at the origin as q1 (+4.11 x 10^-9 C) and the charge at x = +1.00 m as q2 (-2q or -8.22 x 10^-9 C).

The distance between the charges is half of the total distance between them, which is 1 m. So, the distance (r) from each charge to the midway point is 0.5 m.

Using the formula, we can calculate the electric potential due to each charge:

For q1 at the origin:
V1 = (8.99 x 10^9 N m^2/C^2) * (+4.11 x 10^-9 C) / (0.5 m)

For q2 at x = +1.00 m:
V2 = (8.99 x 10^9 N m^2/C^2) * (-8.22 x 10^-9 C) / (0.5 m)

To find the electric potential at the midway point, add V1 and V2:

V_midway = V1 + V2

(b) Find the value of x where the electric potential vanishes:
To find the point where the electric potential vanishes, we need to set the total electric potential to zero and solve for x.

Using the same formula:

V = (8.99 x 10^9 N m^2/C^2) * (+4.11 x 10^-9 C) / (x) + (8.99 x 10^9 N m^2/C^2) * (-8.22 x 10^-9 C) / (1 - x)

Setting V to zero and solving for x will give us the point where the electric potential vanishes.