Magnetic Effects of Electric Current — Karnataka (SSLC) Class 10 Science Solutions (Free)

A magnetic field is the region of space around a magnet or a current-carrying conductor within which a magnetic force can be detected — for example, by a compass needle deflecting or by another current-carrying wire experiencing a force. Field due to a straight conductor: When current flows through a long straight wire, it produces a magnetic field in the form of concentric circles centred on the wire, lying in planes perpendicular to it. The field strength at a perpendicular distance r from the wire is given by B = μ₀I/(2πr), where I is the current and μ₀ is the permeability of free space — so the field gets weaker the further you move from the wire, and stronger with more current. Direction — the Right-Hand Thumb Rule: If you grip the wire with your right hand so that your thumb points in the direction of conventional current flow, your curled fingers point in the direction of the magnetic field lines. This is why a compass placed near a current-carrying wire is deflected, and why the deflection reverses if the current direction is reversed — Oersted's original 1820 experiment that first revealed the connection between electricity and magnetism.

Fleming's Left-Hand Rule: hold the thumb, first finger and second finger of the left hand mutually perpendicular to each other. Point the First finger in the direction of the magnetic Field, the seCond finger in the direction of the Current, and the thuMb then points in the direction of the resulting Motion (force). The force itself: A current-carrying conductor placed in a magnetic field experiences a force given by F = BIL sinθ, where B is the magnetic field strength, I is the current, L is the length of the conductor in the field, and θ is the angle between the current direction and the field direction. - The force is maximum when the conductor is perpendicular to the field (θ = 90°, sinθ = 1), giving F = BIL. - The force is zero when the conductor lies along the field direction (θ = 0°, sinθ = 0) — no force acts, because the conductor's current isn't cutting across any field lines. This is the exact force that makes an electric motor turn — coils in a motor are positioned so a section of the coil is always roughly perpendicular to the field, keeping this force near its maximum.

An electric motor converts electrical energy into mechanical (rotational) energy using the force a magnetic field exerts on a current-carrying conductor. How it works: A rectangular coil is placed between the poles of a magnet, with its two ends connected to a current source through a split-ring commutator and brushes. When current flows, opposite sides of the coil carry current in opposite directions relative to the field. By Fleming's Left-Hand Rule, this means the two sides experience force in opposite directions — one side is pushed up while the other is pushed down — which together create a turning force (torque) that rotates the coil. The role of the split-ring commutator: As the coil turns past the vertical position, the torque would naturally reverse and start slowing the coil back down if the current direction stayed the same. The split-ring commutator is built in two halves, so that exactly at this point, each half swaps which brush it touches — reversing the current direction through the coil at that instant. This keeps the torque acting in the same rotational sense on every half-turn, so the coil keeps spinning continuously in one direction instead of oscillating back and forth.

Electromagnetic induction is the phenomenon in which an electromotive force (EMF), and hence a current if the circuit is closed, is induced in a conductor whenever the magnetic flux linked with it changes. Faraday's Law: The magnitude of the induced EMF is directly proportional to the rate of change of magnetic flux linked with the circuit: ε = −N(dΦ/dt) where N is the number of turns in the coil, Φ is the magnetic flux through one turn (Φ = B·A for a field perpendicular to the coil's area), and dΦ/dt is the rate at which that flux changes with time. The negative sign is Lenz's Law: it states that the induced current always flows in a direction that opposes the change in flux that produced it — this is why, for example, pushing a magnet into a coil faster makes it feel harder to push, since the induced current creates a magnetic field resisting the magnet's motion. This principle is the basis for both AC generators (mechanical rotation changing flux to produce EMF) and transformers (a changing current in one coil inducing EMF in a nearby coil).

Galvanometer: a sensitive instrument that detects and gives a rough, non-calibrated indication of the presence and direction of small electric currents — it cannot, by itself, measure current or voltage on a fixed numerical scale. Ammeter: measures the current flowing through a circuit, and must be connected in SERIES so the full current to be measured passes through it. An ideal ammeter has very low (ideally zero) resistance, so that inserting it into the circuit does not itself reduce the current being measured. Voltmeter: measures the potential difference (voltage) between two points, and must be connected in PARALLEL across those points. An ideal voltmeter has very high (ideally infinite) resistance, so that connecting it draws negligible current and doesn't disturb the circuit it is measuring. Converting a galvanometer: - Into an ammeter: connect a low-resistance shunt in PARALLEL with the galvanometer. Most of the current bypasses the galvanometer through the shunt, letting it safely measure much larger currents while the shunt's low resistance keeps the ammeter's overall resistance low. - Into a voltmeter: connect a high-resistance multiplier resistor in SERIES with the galvanometer. This limits the current through the galvanometer to a safe level even at higher voltages, and the added series resistance gives the combined instrument the high resistance a voltmeter needs.

An AC generator converts mechanical energy into electrical energy using electromagnetic induction — it is essentially an electric motor run in reverse. How it works: A rectangular coil is mechanically rotated (by a turbine, water wheel, or engine) inside a magnetic field. As the coil rotates, the angle between the coil and the field continuously changes, so the magnetic flux through the coil continuously changes too. By Faraday's Law, this changing flux induces an EMF in the coil. Because the coil's orientation relative to the field varies sinusoidally as it spins, the induced EMF also varies sinusoidally with time: ε = ε₀ sin(ωt) where ε₀ is the peak EMF and ω is the angular frequency of rotation. Since the coil's ends are connected to the external circuit through slip rings (not a split-ring commutator, unlike a DC motor), the current in the external circuit reverses direction every half-rotation — this is why the output is called alternating current (AC). Frequency: Frequency (f) is the number of complete cycles of alternation the EMF (or current) completes per second, measured in hertz (Hz). In India, the mains AC supply has a frequency of 50 Hz, meaning the current completes 50 full cycles, and reverses direction 100 times, every second. The corresponding time period is T = 1/f = 1/50 = 0.02 seconds per cycle.

Given: N = 500 turns, A = 0.1 m², B = 0.5 T, f = 50 Hz. Step 1: Find the angular frequency ω = 2πf = 2π × 50 = 314.16 rad/s Step 2: Apply the peak EMF formula for a rotating coil ε₀ = NABω Step 3: Substitute the values ε₀ = 500 × 0.1 × 0.5 × 314.16 ε₀ = 25 × 314.16 ε₀ = 7,854 V ≈ 7.85 kV The peak EMF induced is approximately 7,854 volts.

Given: I = 5 A, L = 0.3 m, B = 0.4 T, and the conductor is perpendicular to the field, so θ = 90°. Using F = BIL sinθ: F = 0.4 × 5 × 0.3 × sin90° F = 0.4 × 5 × 0.3 × 1 F = 0.6 N The force on the conductor is 0.6 newtons.

Given: N = 200 turns, initial flux Φ₁ = 0.002 Wb, final flux Φ₂ = 0.008 Wb, time dt = 0.5 s. Change in flux: dΦ = Φ₂ − Φ₁ = 0.008 − 0.002 = 0.006 Wb Using the magnitude of Faraday's law, ε = N(dΦ/dt): ε = 200 × (0.006 / 0.5) ε = 200 × 0.012 ε = 2.4 V The magnitude of the induced EMF is 2.4 volts.