hi! i am having so much trouble understanding 2 problems from our module, and i would just like some guidance from anyone here! any help is appreciated! thank you in advance and sorry for the trouble.
first is:
A particle of charge 3x10^-9 C is located at point (0,0) in a certain coordinate system. Assuming all lengths are in meters, calculate the potential at the following points: A (3,3) and B (0,2). How much work is needed to take a particle of charge 2x10^-5 C from point A to point B?
and the second one is:
Equal charges of 3x10^-9 C are situated at the three corners of a square of side 5.20 m. Find the potential at the unoccupied corner.
the first one: Potential is V=kq/distance q is the charge, distance is frm the origin to pt A or B.
so the distance from 0,0 to 3,3 is sqrt (9+9) or 3 sqrt2 You know k, and q.
work needed from A to B is (Vb-Va)q
the second Same as the first, except you have different distances, you add them, potenial is not a vector
V= (V1 + V2 + V3) where the Vi is the potential at the unoccupied corner due to the charge at the first corner.
thank you so much! i think i can understand it better now :))
First the really easy part.
Once you have the potential (Voltage) at A and at B
THAT IS the work needed to bring a ONE Coulomb charge from A to B.
B is closer to the + charge at (0,0) so it will take positive work to move a plus charge from A to B with a plus moving charge in your hand.
Now A is how far from (0,0)?
sqrt (3^2+3*2) = 3 sqrt 2
Voltage (potential) at A = 9*10^9 (3*10^-9) / 3sqrt2
Voltage (potential) at B = 9*10^9 (3*10^-9) / 2
work done = charge * change in voltage = 2*110^-5 (Vb-Va)
Hi there! I'd be happy to help you with both of these problems. Let's tackle them one by one.
First problem:
To find the potential at points A (3,3) and B (0,2), we can use the formula for electric potential due to a point charge. The formula is:
V = k * Q / r
Where:
V = electric potential
k = Coulomb's constant, approximately equal to 9 x 10^9 Nm^2/C^2
Q = charge of the particle
r = distance from the particle to the point where we want to find the potential
For point A (3,3):
The distance from the particle to point A is the square root of ((3-0)^2 + (3-0)^2) = sqrt(18) = 4.24 meters. Therefore, the potential at point A is:
V_A = (9 x 10^9 Nm^2/C^2) * (3 x 10^-9 C) / 4.24 m
For point B (0,2):
The distance from the particle to point B is the square root of ((0-0)^2 + (2-0)^2) = sqrt(4) = 2 meters. Therefore, the potential at point B is:
V_B = (9 x 10^9 Nm^2/C^2) * (3 x 10^-9 C) / 2 m
Now, to calculate the work needed to move a particle of charge 2 x 10^-5 C from point A to point B, we can use the formula:
W = q * (V_B - V_A)
Where:
W = work done
q = charge of the particle
V_B = potential at point B
V_A = potential at point A
Substituting the values, we have:
W = (2 x 10^-5 C) * ((9 x 10^9 Nm^2/C^2) * (3 x 10^-9 C) / 2 m - (9 x 10^9 Nm^2/C^2) * (3 x 10^-9 C) / 4.24 m)
Simplifying and calculating this expression will give you the work needed to move the particle from point A to point B.
Second problem:
To find the potential at the unoccupied corner of the square, we can consider the contributions from each of the three charges. The formula for electric potential due to a point charge is the same as mentioned earlier.
We have three charges of 3 x 10^-9 C situated at the corners of a square. The distance between each charge and the unoccupied corner is equal to the side length of the square.
Calculating the potential due to each charge and adding them together will give us the total potential at the unoccupied corner. The formula for the total potential is:
V_total = V1 + V2 + V3
Where:
V_total = total potential at the unoccupied corner
V1, V2, V3 = potential due to each charge
Using the formula mentioned earlier, you can calculate the potential due to each charge. The distance (r) from each charge to the unoccupied corner is equal to the side length of the square. Plug in the values and calculate the potentials due to each charge, and then add them together to find the total potential at the unoccupied corner.
I hope this helps! Let me know if you have any other questions.