Electric potential at a point between 3 point charges

In summary, the conversation discusses a homework problem involving three point charges located at different points on an x-y coordinate system. The goal is to find the total electric potential at a specific point and determine the value of x that would make the potential at that point equal to 0. The attempt at a solution involves using the equation Vp = V1 + V2 + V3, where V is the electric potential and k is a constant. However, the provided solution is incorrect and should instead use the equation V = k * q / r, where q is the charge and r is the distance. The correct solution involves taking into account the distances between the charges and the point in question.
  • #1
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Homework Statement



Three pointcharges are located at the following points on an x-y coordinate system, Q1 = -3 uC at (0,0) q2 = 10.0 uc at (0,0.5m), and q3 = -3 uC at (x,0) . What is the total electric potential at the point (x/2,0) where x is in units of m. At what value does x have to be, for the potential at point (x/2,0) =0

Homework Equations



Vp =V1+v2+v3
V= k * q/r

The Attempt at a Solution


V= k([-3/(x/2)) + (10/(sq rt (.5 =(x/2)))+(-3/(x/2))

Am I going about this wrong? Should i do a vector analysis of the electric field? How do i get this to all = 0?
 
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  • #2
V= k([-3/(x/2)) + (10/(sq rt (.5 =(x/2)))+(-3/(x/2))
It is wrong.
It should be
V= k([-3/(x/2)] + 10/sq rt[ (.5)^2 +(x/2)^2]+(-3/(x/2))*10^-6
 
  • #3


Your approach using the electric potential equation is correct, but there are a few errors in your calculations. Firstly, the distance between the point (x/2,0) and the point (0,0) is not x/2, it is actually (x/2)^2 + 0^2 = (x/2)^2. Secondly, the distance between the point (x/2,0) and the point (0,0.5m) is not sqrt(0.5), it is actually sqrt((x/2)^2 + (0.5)^2). So the correct equation for the electric potential at point (x/2,0) would be:

Vp = k * (-3/(x/2)^2) + k * (10/sqrt((x/2)^2 + (0.5)^2)) + k * (-3/x)

To find the value of x at which the potential at point (x/2,0) is equal to 0, you can set the above equation equal to 0 and solve for x. This will give you the value of x at which the electric potential at that point is 0. Alternatively, you can also use a vector analysis of the electric field at that point to find the value of x at which the electric potential is 0. Both approaches will give you the same answer.
 

What is electric potential at a point between 3 point charges?

The electric potential at a point between 3 point charges is the amount of electric potential energy per unit charge at that point. It is a measure of the electric potential energy that a test charge would have if placed at that point.

How is electric potential at a point between 3 point charges calculated?

The electric potential at a point between 3 point charges can be calculated using the equation V = kq/r, where V is the electric potential, k is the Coulomb's constant, q is the charge of the point charge, and r is the distance from the point charge to the point where the electric potential is being measured.

Can the electric potential at a point between 3 point charges be negative?

Yes, the electric potential at a point between 3 point charges can be negative. This indicates that the electric potential energy at that point is negative, meaning that work would need to be done to bring a positive test charge from infinity to that point.

What factors affect the electric potential at a point between 3 point charges?

The electric potential at a point between 3 point charges is affected by the magnitude of the charges, the distance between the charges, and the medium in which the charges are located. It is also influenced by the presence of other charges in the vicinity.

Can the electric potential at a point between 3 point charges be zero?

Yes, the electric potential at a point between 3 point charges can be zero. This means that the electric potential energy at that point is zero, indicating that no work would need to be done to bring a positive test charge from infinity to that point.

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