Maxwells Equations Conceptual - UNSOLVED PRACTICE SET

Q7. State Gauss's law for electricity in mathematical form and explain its physical significance.

Q8. State Gauss's law for magnetism. Why does it imply that magnetic monopoles do not exist?

Q9. Write Faraday's law of electromagnetic induction in differential form. What does it tell us about the relationship between electric and magnetic fields?

Q10. Write the Ampere-Maxwell law. Explain why Maxwell added the displacement current term.

Q11. How do Maxwell's equations show that electric and magnetic fields are interdependent?

Q12. What is the significance of the constant c (speed of light) appearing in the electromagnetic wave equation derived from Maxwell's equations?

Q13. State and explain all four of Maxwell's equations in integral form. Describe the physical meaning of each equation and identify which experimental law each equation represents.

Q14. Explain how Maxwell's equations lead to the prediction of electromagnetic waves. Show that the wave equations for E and B fields predict waves travelling with speed c = 1/√(μ₀ε₀).

Q15. Discuss the symmetry present in Maxwell's equations. How did the introduction of displacement current complete the symmetry between electricity and magnetism?

Q16. Using Maxwell's equations, show that in free space, the electric field satisfies the wave equation:

∇2E=μ0​ε0​∂t2∂2E​

(a) Starting from Faraday's law and Ampere-Maxwell law, derive this wave equation.

(b) Calculate the value of 1/√(μ₀ε₀) using μ₀ = 4π × 10⁻⁷ H/m and ε₀ = 8.85 × 10⁻¹² F/m.

(c) What is the physical significance of this calculated value?

Q17. A plane electromagnetic wave in vacuum has an electric field amplitude of 100 V/m and frequency 10⁹ Hz.

(a) Calculate the wavelength of the wave.

(b) Calculate the amplitude of the magnetic field.

(c) Write the expressions for E and B fields as functions of position and time.

(d) Verify that these expressions satisfy Maxwell's wave equations.

Q18. In your school's science exhibition, a student creates a poster titled "Maxwell's Legacy" showcasing how his four equations changed the world.

(a) The student writes that Maxwell's first equation (Gauss's law for electricity) explains why a charged balloon sticks to a wall. Explain how this is related to Gauss's law.

(b) She also mentions that Maxwell's second equation explains why compass needles always point north. Is this statement accurate? Correct it if necessary and explain the right connection.

(c) The student claims that without Maxwell's addition of displacement current, we wouldn't have mobile phones today. Discuss whether you agree with this statement and explain the connection between displacement current and wireless communication.

(d) Calculate the speed of electromagnetic waves in a medium with relative permittivity ε_r = 4 and relative permeability μ_r = 1. Compare this with the speed in vacuum.