Chapter Notes

Magnetic Effects of Electric Current

In the previous chapter, we learned that electric current can produce a heating effect. Another important effect is that an electric current-carrying wire behaves like a magnet. This observation reveals a deep connection between electricity and magnetism, a relationship first clearly demonstrated by scientist Hans Christian Oersted.

In 1820, Hans Christian Oersted discovered by accident that a compass needle was deflected when an electric current passed through a nearby wire. This simple experiment showed that electricity and magnetism were related phenomena. His work paved the way for technologies like radio, television, and fiber optics. The unit of magnetic field strength is named the oersted in his honor.

Magnetic Field and Field Lines

We know that a compass needle gets deflected when brought near a bar magnet. This is because a compass needle is itself a tiny bar magnet.

• The end of the needle that points towards the geographic north is called the north seeking or north pole.
• The end that points towards the south is called the south seeking or south pole.

A fundamental property of magnets is that like poles repel, while unlike poles attract each other.

The region surrounding a magnet where its force can be detected is said to have a magnetic field. This field is what causes other magnets or magnetic materials, like iron filings, to experience a force. When iron filings are sprinkled around a bar magnet, they arrange themselves in a distinct pattern. These patterns reveal the magnetic field lines.

Magnetic field lines are imaginary lines used to represent the magnetic field around a magnet.

Properties of Magnetic Field Lines

• Direction: The direction of the magnetic field at any point is shown by the direction a north pole would move if placed there. By convention, field lines emerge from the north pole and merge at the south pole outside the magnet.
• Path: Inside the magnet, the field lines travel from the south pole to the north pole. Therefore, magnetic field lines are closed curves.
• Strength: The strength of the magnetic field is indicated by how close the field lines are to each other. Where the lines are crowded, the field is strong (e.g., near the poles). Where they are far apart, the field is weak.
• Non-Intersection: No two field lines ever cross each other. If they did, it would mean that at the point of intersection, a compass needle would point in two different directions, which is impossible.

A magnetic field is a quantity that has both magnitude (strength) and direction.

Magnetic Field due to a Current-Carrying Conductor

Oersted's experiment showed that an electric current produces a magnetic field. The characteristics of this field depend on the shape of the conductor carrying the current.

Magnetic Field due to a Current through a Straight Conductor

When current flows through a long, straight wire, the magnetic field lines form a pattern of concentric circles around the wire.

The strength of the magnetic field produced depends on two factors:

1. Current: The magnitude of the magnetic field at a given point increases as the current through the wire increases.
2. Distance: The magnetic field produced by a given current decreases as the distance from the wire increases.

Reversing the direction of the current will also reverse the direction of the magnetic field lines.

Right-Hand Thumb Rule

A simple way to find the direction of the magnetic field around a current-carrying conductor is the Right-Hand Thumb Rule.

• Imagine holding a straight current-carrying wire in your right hand.
• Point your thumb in the direction of the current.
• Your fingers will wrap around the conductor in the direction of the magnetic field lines.

This rule is also known as Maxwell's corkscrew rule.

Solution

The current is flowing from east to west.

1. Point directly below the wire: Using the right-hand thumb rule, point your thumb towards the west. Your fingers will curl around the wire. Below the wire, your fingers point towards the south. So, the magnetic field direction is from north to south.

2. Point directly above the wire: With your thumb still pointing west, your fingers above the wire point towards the north. So, the magnetic field direction is from south to north.

Magnetic Field due to a Current through a Circular Loop

If a straight wire is bent into a circular loop and current is passed through it, a magnetic field is produced.

• At every point on the loop, the magnetic field lines are concentric circles.
• As we move towards the center of the loop, the circles become larger and larger.
• At the very center of the loop, the magnetic field lines appear as straight lines.
• Using the Right-Hand Thumb Rule on any section of the loop, we find that the magnetic field lines inside the loop are all in the same direction.

The strength of the magnetic field produced by a current-carrying circular coil depends on:

• Current: The field is directly proportional to the current passing through it.
• Number of turns: If the coil has $n$ turns, the field produced is $n$ times larger than that produced by a single turn, because the fields from each turn add up.

Magnetic Field due to a Current in a Solenoid

A solenoid is a coil of many circular turns of insulated copper wire wrapped closely in the shape of a cylinder.

When current flows through a solenoid:

• The magnetic field pattern is very similar to that of a bar magnet, with one end acting as a north pole and the other as a south pole.
• Inside the solenoid, the magnetic field lines are in the form of parallel straight lines. This indicates that the magnetic field is uniform (the same strength at all points) inside the solenoid.

A strong magnetic field inside a solenoid can be used to magnetize a piece of magnetic material, like soft iron. The magnet created this way is called an electromagnet.

Force on a Current-Carrying Conductor in a Magnetic Field

We have learned that an electric current creates a magnetic field, which can exert a force on a magnet. French scientist Andre Marie Ampere suggested the reverse must also be true: a magnet must exert an equal and opposite force on a current-carrying conductor.

When a current-carrying conductor is placed in a magnetic field, it experiences a force.

• The direction of this force depends on both the direction of the current and the direction of the magnetic field.
• Reversing the direction of the current reverses the direction of the force.
• Reversing the direction of the magnetic field also reverses the direction of the force.
• The force is largest when the direction of the current is at a right angle ($90^\circ$) to the direction of the magnetic field.

Fleming's Left-Hand Rule

To find the direction of the force on the conductor, we use Fleming's Left-Hand Rule.

1. Stretch the thumb, forefinger, and middle finger of your left hand so that they are mutually perpendicular to each other.
2. Point the Forefinger in the direction of the magnetic Field.
3. Point the Middle finger in the direction of the Current.
4. The Thumb will then point in the direction of the Motion or Force on the conductor.

Devices like electric motors, loudspeakers, and microphones work on the principle that a current-carrying conductor in a magnetic field experiences a force.

Solution

The correct answer is (d) into the page.

Here's why: We use Fleming's Left-Hand Rule to find the direction of the force.

• Magnetic Field: The forefinger points from left to right.
• Current: The electron is moving from top to bottom. However, the direction of conventional current is taken as opposite to the direction of motion of electrons. Therefore, the current is directed from bottom to top. Point the middle finger upwards.
• Force: With the forefinger pointing right and the middle finger pointing up, the thumb points into the page.

Therefore, the force on the electron is directed into the page.

Domestic Electric Circuits

In our homes, electric power is supplied through a main supply, which consists of three types of wires:

• Live wire (or positive): Usually has red insulation.
• Neutral wire (or negative): Usually has black insulation.
• Earth wire: Has green insulation.

In our country, the potential difference between the live and neutral wires is $220$ V.

The earth wire is a safety measure, especially for appliances with a metallic body (like refrigerators or toasters). It is connected to a metal plate buried deep in the earth. If there is any leakage of current to the metallic body of the appliance, the earth wire provides a low-resistance path for the current to flow to the earth. This prevents the user from getting a severe electric shock.

In a house, appliances are connected in parallel to each other. This ensures that each appliance receives the full potential difference of $220$ V.

Safety in Circuits

Two common safety issues in domestic circuits are overloading and short-circuiting.

• Overloading can occur when too many high-power appliances are connected to a single socket or when there is an accidental hike in the supply voltage.
• Short-circuiting occurs when the live wire and the neutral wire come into direct contact, often due to damaged insulation. This causes the current in the circuit to increase abruptly to a very high value.

To prevent damage from these situations, an electric fuse is used. A fuse is a safety device that contains a wire with a low melting point. When an unduly high current flows through the circuit (due to overloading or short-circuiting), the Joule heating effect melts the fuse wire, breaking the circuit and stopping the flow of current. This protects the appliances and the house wiring from damage.