Magnetic Effects of Electric Current

Two safety measures commonly used in electric circuits and appliances:

1. Electric Fuse: A fuse is a short piece of wire made of a material with low melting point (e.g., tin-lead alloy). When an excessively large current flows through the circuit (due to overloading or short circuit), the fuse wire heats up and melts, thereby breaking the circuit and protecting the appliances.

2. Earthing (Earth Wire): The metallic body of an appliance is connected to the earth through a green-insulated earth wire. If any leakage of current occurs to the metallic body of the appliance, the current is safely conducted to the earth, preventing the user from receiving an electric shock.

Given:
- Power of electric oven, $P = 2\,\text{kW} = 2000\,\text{W}$
- Voltage of domestic supply, $V = 220\,\text{V}$
- Current rating of circuit, $I_{\text{rated}} = 5\,\text{A}$

Formula used:
$$P = V \times I \implies I = \frac{P}{V}$$

Calculation:
$$I = \frac{2000\,\text{W}}{220\,\text{V}} = 9.09\,\text{A}$$

Result: The current required by the oven ($\approx 9.09\,\text{A}$) is much greater than the current rating of the circuit (5 A).

Explanation: Since the current drawn ($9.09\,\text{A}$) exceeds the safe current rating (5 A) of the circuit, the circuit will be overloaded. This will cause the fuse wire to heat up and melt (blow), thereby breaking the circuit. The oven will not operate, and the circuit is protected from damage.

Precautions to avoid overloading of domestic electric circuits:

1. Do not connect too many appliances to a single socket or a single circuit simultaneously.
2. Do not use appliances with power ratings higher than the current-carrying capacity of the circuit wiring.
3. Ensure proper insulation of all wires so that the live wire and neutral wire do not come into direct contact (which causes short-circuiting).
4. Use proper fuses or MCBs (Miniature Circuit Breakers) of appropriate ratings in the circuit so that excess current automatically breaks the circuit.
5. Avoid using faulty appliances that may draw excessive current due to internal faults.

Correct option: (d) The field consists of concentric circles centred on the wire.

Justification: When current flows through a long straight wire, the magnetic field lines form closed concentric circles in planes perpendicular to the wire, with the wire at their centre. The direction of these circles is given by the Right-Hand Thumb Rule: if the thumb of the right hand points in the direction of current, the curled fingers indicate the direction of the magnetic field lines (concentric circles around the wire).

Correct option: (c) increases heavily.

Justification: A short circuit occurs when the live wire and the neutral wire come into direct contact, reducing the resistance of the circuit to nearly zero. By Ohm's law, $I = V/R$; when $R \approx 0$, the current $I$ becomes very large (increases heavily), which can damage appliances and may cause fire.

(a) True.

Explanation: At the centre of a long circular coil (solenoid), the magnetic field lines are nearly parallel and straight, directed along the axis of the coil. This is because the curved portions of the field lines from each turn add up to give a uniform field at the centre, similar to the field inside a bar magnet.

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(b) False.

Explanation: In domestic electric supply, the wire with green insulation is the earth wire, not the live wire. The live wire has red insulation, and the neutral wire has black insulation. The earth wire is connected to the ground as a safety measure.

Two methods of producing magnetic fields:

1. Using a permanent magnet: A bar magnet or any permanent magnet creates a magnetic field in the region surrounding it. The field lines run from the north pole to the south pole outside the magnet.

2. Using a current-carrying conductor (Electromagnetism): When electric current flows through a conductor (straight wire, circular coil, or solenoid), it produces a magnetic field around it. This is the principle of an electromagnet. The strength of the field can be increased by increasing the current or the number of turns in the coil.

Answer:

The force experienced by a current-carrying conductor placed in a magnetic field is largest when the direction of the current is perpendicular (at 90°) to the direction of the magnetic field.

Explanation: The force on a current-carrying conductor in a magnetic field is given by:
$$F = BIL\sin\theta$$
where $B$ = magnetic field strength, $I$ = current, $L$ = length of conductor, and $\theta$ = angle between the direction of current and the magnetic field.

The force is maximum when $\theta = 90°$, because $\sin 90° = 1$, giving:
$$F_{\text{max}} = BIL$$

When the current is parallel to the field ($\theta = 0°$ or $180°$), the force is zero.

Given:
- Electron beam moves from the back wall to the front wall (i.e., away from you, let us say in the direction forward/north).
- The beam is deflected to the right.

Step 1: Find the direction of conventional current.

Electrons move from back wall to front wall (forward direction). Since conventional current is opposite to the direction of electron flow, the conventional current flows from front wall to back wall (i.e., towards you / backward).

Step 2: Apply Fleming's Left-Hand Rule.

Fleming's Left-Hand Rule states: Stretch the thumb, index finger, and middle finger of the left hand mutually perpendicular to each other.
- Middle finger → direction of conventional current = towards you (backward)
- Thumb → direction of force/deflection = to your right
- Index finger → direction of magnetic field = vertically downward

Conclusion: The direction of the magnetic field is vertically downward (i.e., towards the ground).

(i) Right-Hand Thumb Rule (for magnetic field around a straight current-carrying conductor):

Imagine holding the current-carrying straight conductor in your right hand such that the thumb points in the direction of the current. Then the fingers curled around the conductor indicate the direction of the magnetic field lines (concentric circles) around the conductor.

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(ii) Fleming's Left-Hand Rule (for force on a current-carrying conductor in a magnetic field):

Stretch the thumb, index finger, and middle finger of the left hand such that they are mutually perpendicular to each other.
- The index finger points in the direction of the magnetic field (B).
- The middle finger points in the direction of the current (I).
- The thumb then points in the direction of the force (F) (i.e., motion of the conductor).

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(iii) Fleming's Right-Hand Rule (for direction of induced current in a coil):

Stretch the thumb, index finger, and middle finger of the right hand such that they are mutually perpendicular to each other.
- The index finger points in the direction of the magnetic field (B).
- The thumb points in the direction of motion of the conductor.
- The middle finger then gives the direction of the induced current.

This rule is used in electric generators.

Electric short circuit occurs when the live wire and the neutral wire of an electric supply come into direct contact with each other.

Causes:
1. When the insulation of the live wire and neutral wire is damaged (worn out or broken), they may touch each other directly.
2. When there is a fault inside an appliance that causes the live and neutral connections to touch.

Effect: When a short circuit occurs, the resistance of the circuit becomes almost zero. By Ohm's law ($I = V/R$), the current in the circuit increases to a very large value. This excessive current generates enormous heat, which can damage the wiring, appliances, and may even cause a fire. The fuse in the circuit melts and breaks the circuit to prevent further damage.

Function of Earth Wire:

The earth wire (green insulation) provides a low-resistance conducting path between the metallic body of an appliance and the ground (earth). Its function is to act as a safety device — if any leakage of current occurs to the metallic casing of an appliance (due to damaged insulation or internal fault), the current is immediately conducted safely to the earth through the earth wire instead of passing through the user's body.

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Why it is necessary to earth metallic appliances:

Metallic appliances (such as electric irons, refrigerators, washing machines, geysers) have conducting metal bodies. If the live wire inside the appliance accidentally touches the metal body due to damaged insulation, the entire metallic body becomes live (at 220 V). If a person touches such an appliance, a large current will flow through their body to the ground, causing a severe or fatal electric shock.

By connecting the metal body to the earth through the earth wire, any leakage current flows harmlessly into the ground, keeping the potential of the metallic body at zero (earth potential). This ensures the safety of the user and prevents electric shocks.