Consider the following statements regarding Ampere’s Law:1.Ampere’s circuital law relates line integral of magnetic field around closed path to current enclosed.2.It is useful for symmetric current distributions such as infinite wires and solenoids.3.Ampere’s law is valid only for static fields and not for time-varying fields.4.Magnetic field inside a long solenoid is uniform.Which of the above statements is/are correct?

Correct Answer: D - 1, 2 and 4 only

Quick Concept Explanation

Ampere's circuital law relates circulation of magnetic field to enclosed current for magnetostatic cases. Symmetric geometries such as an infinite straight conductor or long solenoid make the integral law especially useful. Key relation: ∮H·dl=I_enclosed (magnetostatic); ∮H·dl=I_c+d/dt∫D·dS (general form).

Exam focus: For time-varying fields, use the Ampere-Maxwell form. Common trap: Saying Ampere's law has no time-varying extension is incomplete.

Statement-wise Verification

• Statement 1 - Correct.
  Ampere’s circuital law relates line integral of magnetic field around closed path to current enclosed.
  Ampere's circuital law relates circulation of magnetic field to enclosed current for magnetostatic cases.
• Statement 2 - Correct.
  It is useful for symmetric current distributions such as infinite wires and solenoids.
  Symmetric geometries such as an infinite straight conductor or long solenoid make the integral law especially useful.
• Statement 3 - Incorrect.
  Ampere’s law is valid only for static fields and not for time-varying fields.
  The correct principle is: For time-varying fields, use the Ampere-Maxwell form.
• Statement 4 - Correct.
  Magnetic field inside a long solenoid is uniform.
  Ampere's circuital law relates circulation of magnetic field to enclosed current for magnetostatic cases.

Core Concept

Ampere's circuital law relates circulation of magnetic field to enclosed current for magnetostatic cases. Maxwell's displacement-current term extends the relation to time-varying electric fields. Symmetric geometries such as an infinite straight conductor or long solenoid make the integral law especially useful.

Formula / Key Relationship

∮H·dl=I_enclosed (magnetostatic); ∮H·dl=I_c+d/dt∫D·dS (general form).

Why the Other Options Are Wrong

Option A is incorrect because it includes incorrect statement(s) 3 and omits correct statement(s) 4. Option B is incorrect because it includes incorrect statement(s) 3. Option C is incorrect because it includes incorrect statement(s) 3 and omits correct statement(s) 1, 4.

Exam Shortcut / Approach

For time-varying fields, use the Ampere-Maxwell form.

Common Mistake

Saying Ampere's law has no time-varying extension is incomplete.

Quick Revision

Ampere-Maxwell Law and Solenoid Field is linked with Ampere's Circuital Law, Magnetostatics and Electromagnetic Fields. For time-varying fields, use the Ampere-Maxwell form.