Problems

1. Compute the electric field at a point 0.5 m from a point charge of \( 4 \, \mu C \).
2. Two point charges, \( q_1 = 3 \, \mu C \) and \( q_2 = -2 \, \mu C \), are 1 m apart. Find the net electric field at the midpoint.
3. A uniform line charge of \( \lambda = 5 \, \mu C/m \) extends along the x-axis from x = 0 to x = 2 m. Find the electric field at x = 3 m.
4. Explain qualitatively the electric field inside and outside a uniformly charged spherical shell.
5. Use superposition to calculate the electric field at a point due to three charges forming an equilateral triangle.
6. A positive test charge is placed in a uniform electric field of 100 N/C. Calculate the force on the test charge if \( q = 2 \, \mu C \).
7. Draw field lines for two equal and opposite point charges separated by 1 m.
8. Discuss how the field changes with distance for a point charge and for an infinite line charge.
9. Calculate flux through a square of side 0.1 m enclosing a point charge of \( 1 \, \mu C \) at its center.
10. Challenge: For a cube enclosing multiple point charges, describe how to apply superposition and Gauss’s Law to find net flux.