Q has a negative charge and is equal to -7.5. It's equidistant from both q1 and q2. q1 is 10 cm away from Q and q2 is 10 cm away from Q. In order for static equilibrium to occur, what charge will q1 and q2 have to be?
I was thinking that it would be positive 7.5 because both sides would be equal to zero. Is that right?
You have to give the directions. Are they on the same side of Q or opposite sides? If opposite then if they are both +something their field is 0 at the origin and if they are both - anything they also cancel
Note they just have to have the same magnitude so their E cancels. They do not have to be 7.5
To solve this problem, you need to use the principle of electric equilibrium. In order for static equilibrium to occur, the net force on Q must be zero. This means that the electric forces due to q1 and q2 must cancel each other out.
The electric force between two charges is given by Coulomb's Law:
F = k * (q1 * q2) / r^2
Where:
- F is the electric force between the charges
- k is the electrostatic constant (9 x 10^9 Nm^2/C^2)
- q1 and q2 are the charges
- r is the distance between the charges
Since Q is equidistant from both q1 and q2, the distance r is the same for both forces.
Now, let's analyze the problem step by step:
1. Since Q has a negative charge, you correctly stated that it is equal to -7.5.
2. We need to find the charges q1 and q2 that will result in a net force of zero on Q.
3. The electric force between Q and q1 will be attractive because they have opposite charges. The force between Q and q2 will also be attractive for the same reason.
4. Since the forces must cancel each other out, the magnitudes of the forces must be equal.
5. Let's use Coulomb's Law to set up the equation:
F1 = F2
k * (Q * q1) / r^2 = k * (Q * q2) / r^2
6. Divide both sides by Q and rearrange the equation:
q1 = q2
7. This indicates that the magnitudes of q1 and q2 must be equal for the forces to cancel out.
Therefore, the charges q1 and q2 should have the same magnitude, which is 7.5. However, the sign of the charges differs because they need to be attractive to Q (since Q is negative). So, q1 and q2 should be -7.5 in order to achieve static equilibrium.
The charges q1 and q2 should be -7.5C each for static equilibrium to occur.