A +8.1 C charge is fixed at the origin of an x-y co-ordinate system, and two pointcharges are fixed on the y axis: q1 = -32 C at y1 = +0.22 m and a positive pointcharge q2 at y2 = +0.31 m. The net electrostatic force exerted on the charge at the originby the other two charges has a magnitude of 29 N and points in the +y direction. Determinethe magnitude of q2.

The problem involves the principle of superposition and Coulomb's law.

Step 1: Write down the known quantities.

• Charge at origin, q0 = +8.1 µC
• Charge q1 = -32 µC at y1 = +0.22 m
• Charge q2 at y2 = +0.31 m
• Net force on q0, F_net = 29 N

Step 2: Write down the equations for the forces. The force exerted by a charge q on another charge Q separated by a distance r is given by Coulomb's law: F = k*|qQ|/r², where k is Coulomb's constant (8.99*10^9 N m²/C²).

The force on q0 due to q1 is F1 = k*|q0q1|/y1². The force on q0 due to q2 is F2 = k*|q0q2|/y2².

Step 3: Write down the equation for the net force. The net force on q0 is the vector sum of the forces due to q1 and q2. Since the forces are along the y-axis, we can add them as scalars, taking into account their directions. The force due to q1 is in the -y direction (since q1 is negative), and the force due to q2 is in the +y direction (since q2 is positive). Therefore, F_net = -F1 + F2.

Step 4: Substitute the known quantities and solve for q2. We know that F_net = 29 N. Substituting the expressions for F1 and F2 from step 2, we get 29 N = -k*|q0q1|/y1² + k*|q0q2|/y2². We can solve this equation for q2.

Step 5: Solve for q2. Rearranging the equation from step 4, we get q2 = [(29 N + k*|q0q1|/y1²)y2²]/(k|q0|). Substituting the known values, we can calculate the value of q2.