The drawing shows a square, each side of which has a length of L = 0.25 m. Two different positive charges q1 and q2 are fixed at the corners of the square. Find the electric potential energy of a third charge q3 = -4.35 10-8 C placed at corner A and then at corner B.
diagonal of the square = 0.25•sqrt2=0.35 m.
point A (top, right)
φ1=k•q1/0.35 =9•10^9•1.5•10^-9/0.35 =38.6 V
φ2=k•q2/0.25 =9•10^9•4•10^-9/0.25 =144 V
φ = φ1+ φ2 = 182.6 V.
PE=q• φ =-4.35•10^-8• 182.6 = -7.94•10^-6 J.
point B (top, left)
φ1=k•q1/0.25 =9•10^9•1.5•10^-9/0.25 =54 V
φ2=k•q2/0.35 =9•10^9•4•10^-9/0.35 =102.9 V
φ = φ1+ φ2 = 156.9 V.
PE=q• φ =-4.35•10^-8• 156.9 = -6.82•10^-6 J.
more info needed
here are the other charges
q1= +1.5e-9
q2=+4.0e10-9
but i need two ansers for the epe of charge 3 at point a and b. do I just multiply the vtotal by q3 then multiply each charge by that to get the numer for pt a and b
To find the electric potential energy of a charge at different corners of the square, we can use the formula:
Electric potential energy (U) = (k * |q1 * q3|) / r1 + (k * |q2 * q3|) / r2
where k is the electrostatic constant, q1, q2, and q3 are the charges, and r1 and r2 are the distances between the charges.
First, let's calculate the electric potential energy when the charge q3 is placed at corner A.
The distance between corners A and the other corners of the square is L. So, r1 = r2 = L.
Using the given values:
L = 0.25 m
q1 = q2 = unknown (we need to find these charges)
Substitute these values into the formula:
U_A = (k * |q1 * (-4.35 * 10^-8 C)|) / L + (k * |q2 * (-4.35 * 10^-8 C)|) / L
Now, let's calculate the electric potential energy when the charge q3 is placed at corner B.
In this case, the distance r1 is still L, and the distance r2 is now sqrt(2) * L (because corner B is sqrt(2) times farther than the other corners on the diagonal of the square).
Substitute these values into the formula:
U_B = (k * |q1 * (-4.35 * 10^-8 C)|) / L + (k * |q2 * (-4.35 * 10^-8 C)|) / (sqrt(2) * L)
To find the charges q1 and q2, we need more information about the system, such as the potential or field at some point.
Electric potential is a scalar, so you add the potential from each of the other charges.
Vtotal=v1+V2=k(q1/distance+q2/distance2)
Now, for the PE, EPE=Vtotal*q3