A charge of 2.1 nC and a charge of 4.7 nC are separated by 57.90 cm. Find the equilibrium position for a -4.7 nC charge. _______________cm from the 2.1 nC charge.
i know you have to use coulomb's law but how can i use it
F1 =F2
k•q1•|q3|/x^2 = k•q2•|q3|/(d-x)^2
where d-x = (0.579 - x ) m
To be ever so much easier to find X for the algebraically challenged.
X= d*SQRT(K*q1*q3)/SQRT(K*q2*q3)+ SQRT(K*q1*q3)
To find the equilibrium position for a -4.7 nC charge, you can use Coulomb's law, which states that the force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
The formula for Coulomb's law is:
F = k * (q1 * q2) / r^2
Where:
- F is the force between the charges,
- k is the electrostatic constant (k = 8.99 x 10^9 Nm^2/C^2),
- q1 and q2 are the magnitudes of the charges, and
- r is the distance between the charges.
To find the equilibrium position, we need to set the force between the charges to zero since the charges are in equilibrium. Therefore, we can set up the equation:
0 = k * (2.1 nC * (-4.7 nC)) / r^2
First, we need to convert the charges to coulombs (C). 1 nC = 1 x 10^-9 C. So, the charges become:
- q1 = 2.1 nC = 2.1 x 10^-9 C
- q2 = -4.7 nC = -4.7 x 10^-9 C
Substituting the values into the equation, we have:
0 = (8.99 x 10^9 Nm^2/C^2) * (2.1 x 10^-9 C * (-4.7 x 10^-9 C)) / r^2
Now, we can solve for the equilibrium distance, r.
0 = (2.1 x 10^-9 C * -4.7 x 10^-9 C) / r^2
To make the calculation easier, let's remove the negative sign:
0 = (2.1 x 10^-9 C * 4.7 x 10^-9 C) / r^2
Cross-multiplying, we get:
0 = 2.1 x 10^-9 C * 4.7 x 10^-9 C
Now, we can solve for r^2:
r^2 = (2.1 x 10^-9 C * 4.7 x 10^-9 C) / 0
Since any number divided by zero is undefined, there is no solution for r^2. This means that there is no equilibrium position for the -4.7 nC charge. The negative charge will be repelled by the 2.1 nC charge, resulting in an infinite distance between them.