Two identical small spherical conductors (point charges), separated by 0.6 m, carry a total charge of 200 mu or micro CC. They repel one another with a force of 120 N. (For the universal constant k use the value 8.99 times 109 N m2/C2.)
I think i am suppose to use E=kQ/r^2 . do I use this for both spheres then add them to equal 200? where does the force come in?
(a) Find the charge on each sphere.
E is the electric field, the force on a point charge of ONE coulomb.
You can do it with E for either charge, ten multiply by the charge on the other (the target) sphere.
Normally though you would just use the Coulomb law form
F = k Q12Q2/r^2
see:
http://teacher.nsrl.rochester.edu/phy122/Lecture_Notes/Chapter22/Chapter22.html
call one charge Q1 and call Q2 = (200*10^-6 - Q1)
To solve this problem, you can use Coulomb's law to find the charge on each of the small spherical conductors. The formula for Coulomb's law is:
F = k * (q1 * q2) / r^2
Where:
- F is the force between the charges,
- k is the universal constant 8.99 × 10^9 N m^2/C^2,
- q1 and q2 are the charges on the conductors,
- r is the distance between the conductors.
In this case, the force between the conductors is given as 120 N, and the distance between them is 0.6 m. We can rearrange the formula to solve for the product of the charges (q1 * q2):
(q1 * q2) = (F * r^2) / k
Substituting the given values:
(q1 * q2) = (120 N * (0.6 m)^2) / (8.99 × 10^9 N m^2/C^2)
Simplifying, we get:
(q1 * q2) = 0.0016 C^2
Since the conductors have the same charge magnitude (they repel each other), we can write:
q1 * q2 = (q1)^2 (as both charges are equal)
(q1)^2 = 0.0016 C^2
Taking the square root on both sides, we get:
q1 = sqrt(0.0016 C^2)
q1 ≈ 0.04 C
Thus, each conductor has a charge of approximately 0.04 C.
To ensure that the total charge on both conductors is 200 μC, you can calculate the total charge by multiplying the charge of one conductor by 2:
Total charge = 2 * 0.04 C
Total charge ≈ 0.08 C
Therefore, the total charge on both conductors is approximately 0.08 C.
So, to answer your question, the equation E = k * Q / r^2 is not directly applicable in finding the charge on the conductors. However, you can use Coulomb's law to determine the relationship between the force, charges, and distance, which helps in finding the value of the charges on the conductors.
Use the formula F=kQ1Q2/r^2.
Q1+Q2=200*10^-6 C
200*10^-6 C - Q1=Q2
substitute Q2 into the top formula and solve the equation.