a Negative Charge of -6.0 x 10^-6 C exerts an attractive force of 65 N on a second charge 0.050 m away. What is the magnitude on the second charge?
Bc bobpursley annoyingly didnt put the answer and I do know the answer (I'm just being lazy looking up answers) here it is
Q1=(-6.0 x 10^-6) Q2=? F=65N d=0.050 m k=(9.0 x 10^-9)
65=(9.0x10^9)((-6.0x10^-6)Q2)/0.050^2
65 x(0.050^2)= 0.1625
0.1625 /(-6.0x10^-6)= (-2.71x10^4)
(-2.71x10^4)/(9.0x10^9)= (-3.0x10^-6)
ans=(-3.0x10^-6)
go thumbs down bobpursley's post
To solve this problem, we can use Coulomb's Law, which states that the force between two charged objects is proportional to the magnitude of their charges and inversely proportional to the square of the distance between them.
Coulomb's Law can be expressed as:
F = k * (|q1| * |q2|) / r^2
where:
F is the force between the charges,
k is the electrostatic constant (9.0 x 10^9 N·m^2/C^2),
|q1| and |q2| are the magnitudes of the charges, and
r is the distance between the charges.
Given:
Charge 1: q1 = -6.0 x 10^-6 C
Distance: r = 0.050 m
Force: F = 65 N
Let's substitute the known values into Coulomb's Law and solve for |q2|:
65 N = (9.0 x 10^9 N·m^2/C^2) * (|q1| * |q2|) / (0.050 m)^2
To isolate |q2|, we need to rearrange the equation:
|q2| = (65 N * (0.050 m)^2) / [(9.0 x 10^9 N·m^2/C^2) * |q1|]
Now let's calculate |q2|:
|q2| = (65 N * (0.050 m)^2) / [(9.0 x 10^9 N·m^2/C^2) * 6.0 x 10^-6 C]
Calculating the result:
|q2| = 0.185 C
Therefore, the magnitude of the second charge is 0.185 C.
To find the magnitude of the second charge, you can use Coulomb's Law, which states that the force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
Coulomb's Law formula is mathematically expressed as:
F = k * (|q1| * |q2|) / r^2
Where:
F is the force between the charges,
k is Coulomb's constant, approximately 9.0 x 10^9 N*m^2/C^2,
|q1| is the magnitude of the first charge,
|q2| is the magnitude of the second charge,
r is the distance between the charges.
In this case, we know the force F, the distance r, and the magnitude of the first charge |q1|. We need to find the magnitude of the second charge |q2|.
First, let's rearrange the formula to solve for |q2|:
|q2| = (F * r^2) / (k * |q1|)
Now, let's substitute the values into the formula:
|q2| = (65 N * (0.050 m)^2) / (9.0 x 10^9 N*m^2/C^2 * 6.0 x 10^-6 C)
Calculating this expression will give us the magnitude of the second charge |q2|.
Coulombs Law:
force=k q2 q1 / distance^2 solve for q2