a charged particle is in point (2, 3, 8) and has a charge Q1 = 5x10-10C. Another particle is at (5,7,0) and has a charge Q2 = 3x10-10C. Calculate how much work needed to move the first particle to the point (0, -7.2) using the electric field
The initial distance between the particles is
Sqrt(9 + 16 +64) = sqrt89 = R1
The final distance between the particles is
Sqrt(25 +196 +4) = sqrt225 = 15 = R2
Calculate the change in potential energy
K Q1 Q2 (1/R1 - 1/R2)
K is the Coulomb constant
You need to state the units for position. Is it meters?
I need to calculate this using the integral formula which is: W = - ∫ F dl = - q ∫ E dl
Where E = 1 / 4piε0 * R(vector) / R^3
I am just confused in what E-field I have to use and do I need to calculate X,Y & Z separately??
And regarding the position of the charges it only says its positions in the room for example charge 1 is : (x,y,z) = (2,-3,8). But it should be in Meters if SI-unit is needed..
The method I described is a shortcut that will give the correct answer. If you are going to use F*dl integrals, you have to specify the path the moviong charge follows, not just the end points. Ultimately, the answer only depends upon how much the distance between the charges changes, and the productof the two charges.
To calculate the work needed to move a charged particle using the electric field, we need to find the electric potential energy difference between the initial and final points.
Given:
Charge of particle 1, Q1 = 5x10^-10 C
Charge of particle 2, Q2 = 3x10^-10 C
The electric potential energy between two charged particles is given by the equation:
U = k * |Q1 * Q2| / r
Where:
k is Coulomb's constant = 9x10^9 Nm^2/C^2
|Q1 * Q2| is the product of the magnitudes of the charges
r is the distance between the charges
In this case, we need to consider the work done by the electric field to move particle 1 from (2, 3, 8) to (0, -7.2). Since the second particle is fixed at (5, 7, 0), the distance between the charges (r) is the distance between the initial and final positions of particle 1.
Using the distance formula:
r = √((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)
Substituting the given values:
r = √((0 - 2)^2 + (-7.2 - 3)^2 + (0 - 8)^2)
r = √((-2)^2 + (-10.2)^2 + (-8)^2)
r = √(4 + 104.04 + 64)
r = √(172.04)
r ≈ 13.11
Now, we can calculate the electric potential energy difference:
ΔU = k * |Q1 * Q2| * (1/r_final - 1/r_initial)
Substituting the values:
ΔU = (9x10^9 Nm^2/C^2) * |(5x10^-10 C) * (3x10^-10 C)| * (1/13.11 - 1/√(2^2 + 3^2 + 8^2))
Simplifying the equation:
ΔU = (9x10^9 Nm^2/C^2) * (15x10^-20 C^2) * (1/13.11 - 1/√77)
ΔU = 122.81 Nm
Hence, the work needed to move the first particle to the point (0, -7.2) using the electric field is approximately 122.81 Nm.