Final answer:
The student's questions involve using principles of superposition to determine points where the net electric and magnetic fields are zero, and using formulas to calculate the electric field magnitude from point charges and the average electric field along a path.
Step-by-step explanation:
The student's question revolves around the concept of establishing a position on the x-axis where the net electric field is zero due to point charges or electric currents. This involves solving problems on electric fields and magnetic fields created by charges and currents, respectively. To find where an electric field is zero, one typically uses the principle of superposition to equate the magnitude of electric fields from multiple point charges and solve for the position. Similarly, the cancellation of the magnetic field at a point due to currents in two wires requires understanding the direction and magnitude of magnetic fields produced by electric currents (using the right-hand rule).
For the electric potential question, the average electric field is found by dividing the potential difference by the distance over which it changes, based on the formula E = \(\Delta V / \Delta x\).
Lastly, calculating the magnitude of the electric field from a point charge is done using Coulomb's law, which states that E = k\(|q| / r^2\), where k is Coulomb's constant, |q| is the magnitude of the charge, and r is the distance from the charge.