Q1 and Q2 are charged objects of the same sign separated by a distance 29.9 m. If you place another charged object (Q3) a distance 8.0 m from Q2 along a direct line between Q1 and Q2, it experiences no net electric field. So, if the magnitude of Q2 = 9.3 C, what is the magnitude of charge Q1?
To find the magnitude of charge Q1, we will use the concept of electrostatic equilibrium, where the net electric field experienced by an object is zero.
In this case, we have three charged objects: Q1, Q2, and Q3. Q1 and Q2 are separated by a distance of 29.9 m, and Q3 is placed 8.0 m away from Q2 along a direct line between Q1 and Q2.
Since we are told that Q3 experiences no net electric field, it means that the electric fields produced by Q1 and Q2 at the location of Q3 must cancel each other out.
The electric field produced by a point charge can be calculated using Coulomb's law: E = k * (Q / r^2), where E is the electric field, k is the electrostatic constant (9 x 10^9 N m^2/C^2), Q is the magnitude of the charge, and r is the distance from the charge.
For Q3 to experience no net electric field, the electric fields produced by Q1 and Q2 at the location of Q3 must be equal in magnitude but opposite in direction.
Therefore, we can set up the following equation:
k * (Q1 / r1^2) = k * (Q2 / r2^2)
In this case, r1 is the distance from Q1 to Q3 (which is the sum of the distances from Q1 to Q2 and from Q2 to Q3), and r2 is the distance from Q2 to Q3.
Substituting the values given:
k * (Q1 / (29.9 + 8.0)^2) = k * (9.3 / 8.0^2)
The electrostatic constant k cancels out on both sides of the equation:
Q1 / (37.9)^2 = 9.3 / 64
Rearranging the equation to solve for Q1:
Q1 = (9.3 / 64) * (37.9)^2
Calculating this expression gives the magnitude of charge Q1.