Magnetic Effects of Electric Current-Notes
Physics - Notes
MAGNETIC FIELD AND FIELD LINES
Definition of magnetic field
A magnetic field is the region around a magnet, a current-carrying conductor, or a moving electric charge where another magnet or magnetic material experiences a magnetic force. In physics, the magnetic field at a point is represented by the vector \(\vec{B}\), where the direction of \(\vec{B}\) shows the direction of the field and its magnitude shows the strength of the field at that point.
The presence of a magnetic field at a point can be detected with a small compass needle. When the compass is placed in the field, its north-seeking pole aligns along the direction of the local magnetic field at that point.
Magnetic field lines: concept
Magnetic field lines (or lines of magnetic force) are imaginary curves drawn in a magnetic field such that the tangent at any point on a field line gives the direction of the magnetic field at that point. These lines help us to represent a three-dimensional magnetic field in a simple two-dimensional diagram.
Each magnetic field line is drawn with an arrowhead to show the direction of the magnetic field. By convention, the direction of a magnetic field line is taken as the direction in which the north pole of a small test magnet would tend to move if placed in the field.
Field lines around a bar magnet
Around a bar magnet, magnetic field lines start from the north pole, curve through the surrounding space, and enter the south pole. Inside the magnet, these lines are taken to move from the south pole back to the north pole. Thus, for a bar magnet, the magnetic field lines form continuous closed loops.
Outside the magnet, the direction of field lines is taken from north to south, while inside the magnet it is from south to north. This continuous looping nature clearly shows that magnetic field lines do not have a beginning or an end; they always form closed paths.
Key properties of magnetic field lines
- Closed loops: Magnetic field lines always form closed loops. For a bar magnet, they emerge from the north pole, travel through the surrounding medium, and enter the south pole, then continue through the magnet’s interior from south to north.
- No intersection: Two magnetic field lines never intersect each other. If they intersected, it would mean that the magnetic field at the point of intersection has two different directions at the same time, which is impossible.
- Direction indication: The arrow on a field line shows the direction of the magnetic field. This is the direction in which the north pole of a small test magnet would move if it were free to do so.
- Field strength and crowding: The density of field lines (how close they are) represents the strength of the magnetic field. Where field lines are crowded together, the magnetic field is strong; where they are widely spaced, the field is weak. This is why field lines are denser near the poles of a bar magnet.
- Continuity and smoothness: Magnetic field lines are smooth, continuous curves; they do not have sharp corners or breaks. They provide a continuous description of how the magnetic field changes from point to point.
MAGNETIC FIELD DUE TO A CURRENT-CARRYING CONDUCTOR
A magnetic field is produced around a current-carrying conductor due to the movement of electric charges (current) through the conductor. This magnetic field exists in the space surrounding the conductor and can exert a force on other magnetic materials or currents placed nearby. The magnetic field produced is circular and concentric around the conductor.
The magnetic field lines around a straight current-carrying conductor form concentric circles with the conductor at the center. The direction of these magnetic field lines can be determined by the Right-Hand Thumb Rule: if you hold the conductor in your right hand with your thumb pointing in the direction of the current, then the curled fingers around the conductor show the direction of the magnetic field lines.
The strength of the magnetic field depends on two main factors:
- The magnitude of the current flowing through the conductor: larger current produces a stronger magnetic field.
- The distance from the conductor: the magnetic field strength decreases as you move farther from the conductor.
Right-Hand Thumb Rule
The Right-Hand Thumb Rule is used to determine the direction of the magnetic field around a current-carrying conductor. It states:
If you hold the conductor with your right hand such that your thumb points in the direction of the conventional current, then your fingers curled around the conductor show the direction of the magnetic field lines.
Steps to apply the rule:
- Grasp the conductor with your right hand.
- Point the thumb in the direction of the current (from positive to negative).
- The curled fingers around the conductor will indicate the direction of the magnetic field.
Example:
For a current flowing upward through a vertical wire, the magnetic field lines around the wire will be in an anticlockwise direction when viewed from above. This follows directly from the right-hand thumb rule, as the curled fingers point anticlockwise around the wire.
This rule is essential to understand magnetic fields created by current-carrying conductors, and is widely used in solving problems related to magnetic effects of electric current.
Magnetic Field due to a Current through a Circular Loop
A current-carrying circular loop produces a magnetic field that is concentrated at the center of the loop. When an electric current flows through the wire shaped into a circular loop, the magnetic field lines form concentric circles around every small segment of the wire. These circles combine to produce a magnetic field that is strongest and nearly uniform at the center of the loop, with the magnetic field lines inside the loop appearing almost straight and perpendicular to the plane of the loop.
The direction of the magnetic field due to a current in a circular loop is found using the Right-Hand Thumb Rule: If you curl the fingers of your right hand in the direction of current flowing through the loop, your thumb points in the direction of the magnetic field at the center of the loop.
Magnetic Field due to a Current in a Solenoid
A solenoid is a long coil of insulated copper wire wound in the shape of a cylinder. When electric current passes through this coil, it produces a magnetic field similar to that of a bar magnet.
Magnetic field pattern
Inside the solenoid, the magnetic field lines are parallel and close to each other. This shows that the magnetic field inside the solenoid is strong and uniform at all points. Outside, the magnetic field lines spread out and form closed loops from one end to the other of the solenoid.
Behavior like a magnet
One end of the solenoid behaves like the north pole and the other like the south pole of a magnet. The magnetic field outside the solenoid is similar to the field of a bar magnet.
Factors affecting magnetic field strength
- Number of Turns: Increasing the number of turns increases the strength of the magnetic field.
- Current Magnitude: Higher current flowing through the solenoid increases the magnetic field strength.
- Core Material: Using a soft iron core inside the solenoid greatly enhances the magnetic field, making the solenoid an electromagnet.
Direction of magnetic field
The direction of the magnetic field produced inside the solenoid can be found using the Right-Hand Thumb Rule. If the fingers of your right hand curl in the direction of current in the coil, your thumb will point towards the solenoid's north pole and direction of the magnetic field inside the coil.
FORCE ON A CURRENT-CARRYING CONDUCTOR IN A MAGNETIC FIELD
When a current flows through a conductor placed in a magnetic field, the conductor experiences a force known as magnetic force. This happens because the magnetic field interacts with moving charges inside the conductor.
Factors Affecting the Force
- The strength of the magnetic field \( B \)
- The amount of current \( I \) flowing through the conductor
- The length \( L \) of the conductor inside the magnetic field
- The angle \( \theta \) between the conductor and the magnetic field direction
Formula for the Force
\[ F = BIL \sin \theta \]
The force is maximum when the conductor is perpendicular to the magnetic field (\( \theta = 90^\circ \)) and zero when it is parallel (\( \theta = 0^\circ \)).
Direction of the Force
The direction of the force is given by Fleming’s Left-Hand Rule: Stretch the thumb, forefinger, and middle finger of your left hand at right angles to each other. If the forefinger points in the direction of the magnetic field and the middle finger in the direction of the current, then the thumb shows the direction of the force on the conductor.
Importance
This force is the working principle behind electric motors, where current-carrying coils in magnetic fields experience forces that cause rotation.
Fleming’s left-hand rule
Fleming’s Left-Hand Rule is used to find the direction of force experienced by a current-carrying conductor when placed in a magnetic field. It helps us determine the direction in which the conductor will move.
To apply this rule, stretch the thumb, forefinger, and middle finger of your left hand so that they are mutually perpendicular (at right angles) to each other.
- Forefinger points in the direction of the magnetic field (from north to south).
- Middle finger points in the direction of the current (from positive to negative).
- Thumb points in the direction of the force or motion experienced by the conductor.
This rule shows that the force on the conductor is always perpendicular to both the magnetic field and the direction of the current.
It is very important in understanding how devices like electric motors work, where the force generated causes continuous rotation.
DOMESTIC ELECTRIC CIRCUITS
Domestic electric circuits are networks of electrical wiring in homes used to distribute electric power safely and efficiently. These circuits enable us to use electrical appliances and devices by connecting them to the power supply.
Components of Domestic Circuits
- Live wire: Carries current from the power source to the appliance.
- Neutral wire: Completes the circuit by carrying current back to the source.
- Earth wire: Provides a low-resistance path to ground for safety during faults.
- Switches: Controls the flow of electric current to appliances.
- Fuses/Circuit breakers: Protect the circuit by breaking the connection when excess current flows.
Safety Measures
Earthing and the use of fuses or circuit breakers are essential for preventing electric shocks and electrical fires. Proper insulation of wires and careful installation ensure safe operation of household electrical devices.
Working Principle
When a switch is turned on, current flows from the live wire to the appliance and returns to the source through the neutral wire, completing the circuit. If any fault occurs, the fuse melts or the circuit breaker trips to stop the current, protecting the wiring and devices.
Important Points
- A compass needle is a small magnet. Its one end, which points towards north, is called a north pole, and the other end, which points towards south, is called a south pole.
- A magnetic field exists in the region surrounding a magnet, in which the force of the magnet can be detected.
- Field lines are used to represent a magnetic field. A field line is the path along which a hypothetical free north pole would tend to move. The direction of the magnetic field at a point is given by the direction that a north pole placed at that point would take. Field lines are shown closer together where the magnetic field is greater.
- A metallic wire carrying an electric current has associated with it a magnetic field. The field lines about the wire consist of a series of concentric circles whose direction is given by the right-hand rule.
- The pattern of the magnetic field around a conductor due to an electric current flowing through it depends on the shape of the conductor. The magnetic field of a solenoid carrying a current is similar to that of a bar magnet.
- An electromagnet consists of a core of soft iron wrapped around with a coil of insulated copper wire.
- A current-carrying conductor when placed in a magnetic field experiences a force. If the direction of the field and that of the current are mutually perpendicular to each other, then the force acting on the conductor will be perpendicular to both and will be given by Fleming’s left-hand rule.
- In our houses we receive AC electric power of 220 V with a frequency of 50 Hz. One of the wires in this supply is with red insulation, called live wire. The other one is of black insulation, which is a neutral wire. The potential difference between the two is 220 V. The third is the earth wire that has green insulation and this is connected to a metallic body deep inside earth. It is used as a safety measure to ensure that any leakage of current to a metallic body does not give any severe shock to a user.
- Fuse is the most important safety device, used for protecting the circuits due to short-circuiting or overloading of the circuits.
