Case Study
Passage with linked questions
Case Set 1
Case AnalysisPassage
A physics teacher demonstrates Oersted's experiment in class. She places a compass needle near a long straight wire connected to a battery. When the switch is closed, the needle deflects noticeably. She then reverses the battery terminals and observes that the needle deflects in the opposite direction. Next, she increases the current by reducing the external resistance, and the deflection increases. She sprinkles iron filings on a horizontal cardboard sheet through which the wire passes vertically, and the filings arrange themselves in concentric circles. She explains that this experiment, first performed in 1820, established the intimate connection between electricity and magnetism, leading eventually to Maxwell's unification of the two phenomena in 1864.
Question 1: What conclusion did Oersted draw from his experiment about the relationship between current and magnetic field?
- Oersted concluded that moving charges or currents produce a magnetic field in the surrounding space around the wire.
- The alignment of the compass needle is tangential to an imaginary circle centred on the wire, with its plane perpendicular to the wire, confirming the field surrounds the wire in closed circular loops.
Question 2: The iron filings arrange in concentric circles around the wire. How does this pattern differ from the pattern formed by iron filings around an electric dipole, and what does this difference signify?
- Around a current-carrying wire, iron filings form closed concentric circles, reflecting that magnetic field lines form closed loops with no starting or ending point.
- Around an electric dipole, field lines originate at the positive charge and terminate at the negative charge; they are open curves. This difference signifies the absence of magnetic monopoles — there is no magnetic equivalent of isolated electric charges.
Question 3: Using Ampere's circuital law, derive the expression for the magnitude of the magnetic field at a perpendicular distance r from the long straight wire carrying current I, and state its direction using the right-hand rule.
- Choose a circular Amperian loop of radius r coaxial with the wire. By cylindrical symmetry, B is tangential and constant in magnitude along the loop, so ∮B·dl = B(2πr).
- The total current enclosed by the loop is I. Applying Ampere's law: B(2πr) = μ₀I, giving B = μ₀I/(2πr). The field is inversely proportional to distance r from the wire.
- Direction by right-hand rule: Grasp the wire in the right hand with the extended thumb pointing in the direction of the current; the fingers curl in the direction of the magnetic field, forming the concentric circular field lines observed with iron filings.