Chapter 4: Magnetic Effects of Electric Current

Solution

Outside a magnet, magnetic field lines always travel from the north pole to the south pole. Inside the magnet, they travel from south to north, completing the closed loop. This is a fundamental property of magnetic field lines — they are continuous closed curves.

Solution

A current-carrying conductor produces a magnetic field (Oersted's discovery). The compass needle, being a tiny magnet, aligns itself along the direction of the resultant magnetic field — which is tangential to the concentric circles of the field around the wire. The deflection proves that electric current produces a magnetic field.

Solution

The magnetic field around a straight current-carrying conductor forms concentric circles in planes perpendicular to the wire. The wire is at the centre of these circles. The direction of these circles can be found using the right-hand thumb rule.

Solution

Right-Hand Thumb Rule: Imagine holding the current-carrying conductor in your right hand such that the thumb points in the direction of the current. Then your fingers naturally curl around the conductor, and the direction in which they curl gives the direction of the magnetic field lines.

For example, if a wire carries current upward (thumb pointing up), the fingers curl in the anti-clockwise direction when viewed from above. So the magnetic field circles the wire in the anti-clockwise direction as seen from the top.

Solution

Inside a long solenoid, the magnetic field is uniform and strong. The field lines inside are parallel and equally spaced, indicating a constant field throughout the interior. This is one of the most important practical sources of a uniform magnetic field. Outside the solenoid, the field is weak and non-uniform.

Solution

In Fleming's left-hand rule:

• Forefinger → magnetic Field direction
• Middle finger → Current direction
• Thumb → Force (or motion) on the conductor

This rule is used for motors (where current and field are given, and we need to find the force/motion direction).

Solution

An electric motor converts electrical energy into mechanical energy (rotational motion). It uses the force experienced by a current-carrying conductor in a magnetic field to produce rotation. The reverse device — a generator — converts mechanical energy into electrical energy.

Solution

Michael Faraday discovered electromagnetic induction in 1831. He showed that a changing magnetic field induces an electric current in a conductor. Oersted discovered that current produces a magnetic field (1820). Ampère studied forces between current-carrying conductors. Fleming formulated the left-hand and right-hand rules.

Solution

Fleming's right-hand rule is used to find the direction of the induced current (or induced EMF) when a conductor moves in a magnetic field. It is used for generators and electromagnetic induction scenarios.

Fleming's left-hand rule is for motors (finding force direction). The right-hand rule is for generators (finding induced current direction). Remember: Left = motor, Right = generator.

Solution

The domestic electric supply in India is 220 V AC at 50 Hz. This means the voltage alternates between +311 V and -311 V (peak values), with an RMS (effective) value of 220 V. The frequency of 50 Hz means the current changes direction 100 times per second (50 complete cycles).

Solution

The earth wire is a safety wire in domestic circuits. Its functions:

• It is connected to the metal body of all electrical appliances (like refrigerator, washing machine, iron).
• Under normal conditions, no current flows through the earth wire.
• If a fault occurs (e.g., the live wire touches the metal body), the earth wire provides a low-resistance path for the current to flow to the ground.
• This large current through the earth wire blows the fuse or trips the MCB, disconnecting the supply.
• Without earthing, the metal body would be at 220 V, and anyone touching it would get a potentially fatal electric shock.

Solution

A short circuit occurs when the live wire and neutral wire come into direct contact, usually due to damaged insulation. This creates a path of very low resistance (almost zero), causing an extremely large current to flow (I = V/R, when R → 0, I → very large). This excessive current generates a lot of heat (H = I²Rt), which can melt wires and start fires. Fuses and MCBs are designed to break the circuit immediately when this happens.

Solution

Magnetic field lines never intersect. If they did, there would be two directions of the magnetic field at the point of intersection, which is impossible — the magnetic field at any point has a unique direction. A compass needle at that point would need to point in two directions simultaneously, which is physically impossible.

Solution

Using Fleming's Left Hand Rule:

Forefinger (field) = downward, Middle finger (current) = east

Thumb (force) = north

Solution

Using Fleming's Left Hand Rule:

Forefinger (field) = east, Middle finger (current) = upward

Thumb (force) = north

Solution

Using Fleming's Left Hand Rule:

Forefinger (field) = upward, Middle finger (current) = east

Thumb (force) = south

Solution

Using Fleming's Left Hand Rule:

Forefinger (field) = north, Middle finger (current) = west

Thumb (force) = downward (vertically)

Solution

Using Fleming's Left Hand Rule:

Forefinger (field) = downward, Middle finger (current) = west

Thumb (force) = south

Solution

Using Fleming's Left Hand Rule:

Forefinger (field) = north, Middle finger (current) = east

Thumb (force) = upward (vertically)

Solution

Using Fleming's Left Hand Rule:

Forefinger (field) = west, Middle finger (current) = north

Thumb (force) = upward (vertically)

Solution

Using Fleming's Left Hand Rule:

Forefinger (field) = east, Middle finger (current) = north

Thumb (force) = downward (vertically)

Solution

Using Fleming's Left Hand Rule:

Forefinger (field) = east, Middle finger (current) = south

Thumb (force) = upward (vertically)

Solution

Using Fleming's Left Hand Rule:

Forefinger (field) = north, Middle finger (current) = upward

Thumb (force) = west

Solution

Why soft iron?

• Soft iron has high magnetic permeability — it gets strongly magnetised by the field of the solenoid, multiplying the field strength many times.
• Soft iron is easily demagnetised when the current is switched off. This is essential — we want the magnetism to disappear when not needed.
• Hard steel would retain magnetism even after the current is off, which is undesirable for an electromagnet.

Advantages of electromagnets:

• Can be switched on and off by controlling the current.
• The strength can be varied by changing the current.
• The polarity can be reversed by reversing the current direction.
• Can be made much stronger than permanent magnets.

Solution

The split ring commutator in a DC motor serves a crucial function: it reverses the direction of current flowing through the coil every half rotation.

Why is this necessary?

• When the coil rotates by half a turn, the arms of the coil swap positions — the arm that was near the north pole is now near the south pole.
• If the current direction remained the same, the force on each arm would reverse, and the coil would start rotating backward. It would just oscillate back and forth.
• The commutator reverses the current at exactly the right moment so that the forces on the arms always push the coil in the same rotational direction.
• This ensures continuous rotation in one direction.

Without the commutator, the motor would not work as a motor — the coil would merely oscillate.

Solution

(a) Magnet is pulled out:

The magnetic flux through the coil is decreasing (opposite change compared to pushing in). The induced current flows in the opposite direction, so the galvanometer shows deflection in the reverse direction.

(b) Magnet is held stationary inside the coil:

The magnetic flux through the coil is not changing (it's constant). Since there is no change in flux, there is no induced EMF and no current. The galvanometer shows zero deflection.

(c) Magnet is pushed in faster:

The rate of change of magnetic flux is greater (flux changes more quickly). This induces a larger EMF and a stronger current. The galvanometer shows a greater deflection.

Solution

Principle: An electric generator works on the principle of electromagnetic induction — when a coil is rotated in a magnetic field, the changing magnetic flux induces an EMF (and current) in the coil.

Differences:

• AC Generator: Uses slip rings (two complete rings). The current in the external circuit reverses direction every half rotation, producing alternating current (AC) that varies sinusoidally.
• DC Generator: Uses a split ring commutator (two half rings). The commutator reverses the connections every half rotation, ensuring the current in the external circuit always flows in one direction — producing direct current (DC).

The fundamental principle is the same — the only difference is in how the current is collected from the rotating coil.

Solution

Using Fleming's Left-Hand Rule:

• Forefinger → magnetic field direction = East to West (point forefinger westward)
• Middle finger → current direction = North to South (point middle finger southward)
• Thumb → this gives the direction of force

When you orient your left hand with the forefinger pointing west and the middle finger pointing south (perpendicular to the forefinger), the thumb points vertically upward.

Therefore, the force on the conductor is directed vertically upward.

Solution

The induced EMF (and hence current) is maximum when the rate of change of magnetic flux is maximum. This happens when the plane of the coil is parallel to the magnetic field (i.e., the coil is at 0° or 180° in its rotation). At this position, the coil arms are cutting through the field lines most rapidly.

When the coil is perpendicular to the field, the flux through it is maximum but its rate of change is momentarily zero — so the induced EMF is zero at that instant.

Solution

The strength of the induced current can be increased by:

• Moving the magnet faster: A greater rate of change of magnetic flux induces a larger EMF and hence a larger current.
• Increasing the number of turns in the coil: More turns means more flux linkage, and the induced EMF is proportional to the number of turns.
• Using a stronger magnet: A stronger magnetic field means a larger change in flux for the same movement, inducing a greater EMF.

These are direct consequences of Faraday's law: the induced EMF is proportional to the rate of change of magnetic flux, which depends on the speed of motion, the field strength, and the number of turns.

Solution

Overloading:

• Occurs when too many appliances are connected to a single circuit simultaneously.
• The total current drawn exceeds the designed capacity of the wiring.
• Wires heat up gradually due to excessive current.

Short Circuit:

• Occurs when the live and neutral wires come into direct contact (due to damaged insulation, loose connections, etc.).
• Creates a near-zero resistance path, causing an extremely large current to flow suddenly.
• Much more dangerous and sudden than overloading.

How a fuse protects:

In both cases, the current exceeds the rated value of the fuse. The excessive current produces heat in the fuse wire (H = I²Rt). Since the fuse wire has a low melting point, it melts and breaks the circuit before the wiring or appliances are damaged. The fuse is always connected in the live wire so that the circuit is completely disconnected from the high-potential wire.

Solution

The magnetic field strength (B) due to a long straight current-carrying conductor at a perpendicular distance r is inversely proportional to the distance (B ∝ 1/r). As you move away from the wire, the concentric field-line circles get larger and farther apart, indicating a weaker field.

The field is also directly proportional to the current: B ∝ I. So increasing the current strengthens the field, and moving away weakens it.

Solution

When the magnet is held stationary inside the coil, there is no change in the magnetic flux linked with the coil. Since electromagnetic induction requires a changing magnetic flux, no EMF is induced, and therefore no current flows. The galvanometer shows zero deflection.

Current is induced only when there is relative motion between the magnet and the coil (i.e., when the flux is changing).

Solution

The magnetic field at the centre of a circular current-carrying loop:

(a) Depends on current: The magnetic field (B) at the centre is directly proportional to the current (I). Doubling the current doubles the field strength. This is because a larger current means more moving charges, producing a stronger magnetic effect.

(b) Depends on radius: The field is inversely proportional to the radius (r) of the loop. A smaller loop produces a stronger field at its centre because the wire (source of the field) is closer to the centre. A larger loop has weaker field at the centre because the wire is farther away.

Additionally, if there are n turns in the loop, the field is n times stronger (B ∝ nI/r).

Solution

Components (for labelled diagram): Rectangular coil ABCD, permanent magnet (N and S poles), split ring commutator (two half-rings C₁ and C₂), carbon brushes B₁ and B₂, battery, axle.

Working:

• Current flows through the coil in the magnetic field.
• By Fleming's left-hand rule, arm AB experiences an upward force and arm CD experiences a downward force (or vice versa).
• These opposite forces create a torque that rotates the coil.
• The coil rotates in one direction (say clockwise).

Why doesn't the coil stop at the vertical position?

At the vertical position, the forces on the arms act along the same line (no torque). However, the split ring commutator reverses the current direction at exactly this position. Due to inertia, the coil moves slightly past the vertical. With the current now reversed, the forces again produce torque in the same rotational direction, pushing the coil through another half-rotation. This process repeats, ensuring continuous rotation.