### 5.4 Magnetic Effects of Electric Circuits

Magnetic field (B)

Poles: North (N) and South (S).

Existence: only if a force acts on a pair of magnetic poles.

Opposite poles attract each other, while like poles repel each other.

Electric currents produce magnetic fields, e.g. Earth’s molten iron core.

Magnetic field lines: Always from North-pole to South-pole.

Similar properties as the electric field lines.

Right-hand grip rule (for wires): “Grip the wire with the fingers of the right hand in such a way that the thumb points in the direction of the [conventional] current. Then the direction in which the fingers curls is the direction of the ‘flow’ of the magnetic field vectors”. (Tsokos, 2014)

Representation of current

Dot: current leaving the page towards you.

Cross: current entering page away from you.

Representation of current and Magnetic field around it.

As the lines are further from the wire, the distance between them increases, as the field becomes weaker.d magnetic field around it

- Solenoid: field runs along its hollow centre and outside it (coil of wire).

Magnetic force on a moving charge

Equation: F = qvBsinθ, where B is the magnetic field strength, q is the charge’s value, v is the speed of the moving charge and θ is the angle its speed has with the magnetic field lines.

Magnetic field strength (B) definition by charges: “Force acting per unit charge per speed, on a positive moving charge perpendicular to the magnetic field.”

There is no magnetic force on a moving charge if the charge moves along the field direction.

Fleming’s left-hand rule for positive moving charges (vectorial product): for negative charges, the force is in the opposite direction.

**Circular path**: When the speed is perpendicular to the magnetic field.

**Helical path**: When the charge enters the field at a certain angle.

### Magnetic force on current-carrying wires

Equation: F = BILsinθ, where B is the magnetic field strength, I is the current on the wire and L is the wire’s length.

Magnetic field strength (B) definition by current: “Force acting per unit current in a wire per unit length, which is perpendicular to the field”. Unit: tesla (T).

Fleming’s left-hand rule for wires with current: vectorial product.

Magnetic force between two current-carrying wires: depends on each wire’s current direction.

If currents are in the same direction: attract!

If currents are in opposite directions: repel!

Magnetic force between a bar magnet and a current: catapult field.

## MOVING CHARGES AND MAGNETISM

### OERSTED EXPERIMENT

### MAGNETIC FIELD

### MAGNETIC FIELD DUE TO CURRENT CARRYING CONDUCTOR, BIOT-SAVART’S LAW

### MAGNETIC FIELD DUE TO VARIOUS CURRENT CARRYING CONDUCTORS

#### MAGNETIC FIELD DUE TO FINITE SIZED CONDUCTOR

#### MAGNETIC FIELD NEAR THE END OF A FINITE SIZED CONDUCTOR

#### MAGNETIC FIELD DUE TO AN INFINITELY LONG CONDUCTOR

#### MAGNETIC FIELD NEAR THE END OF A LONG CONDUCTOR

#### MAGNETIC FIELD DUE TO A CURRENT CARRYING COIL

#### MAGNETIC FIELD INSIDE A CURRENT CARRYING SOLENOID

- Finite size solenoid

- Near the end of a finite solenoid

- In the middle of a very long solenoid, B = μ0 n I
- Near the end of a very long solenoid

- Magnetic field in the endless solenoid (toroid) is same throughout and is μ0nI.
- Magnetic field outside a solenoid or toroid is zero.

### AMPERE’S CIRCUITAL LAW

- The direction of the magnetic field at a point on one side of a conductor of any shape is equal in magnitude but opposite in direction of the field at an equidistant point on the other side of the conductor.
- If the magnetic field at a point due to a conductor of any shape is Bo if it is placed in vacuum then the magnetic field at the same point in a medium of relative permeability μr is given by .
- If the distance between the point and an infinitely long conductor is decreased (or increased) by K-times then the magnetic field at the point increases (or decreases) by K-times.
- The magnetic field at the centre of a circular coil of radius smaller than other similar coil with greater radius is more than that of the latter.
- For two circular coils of radii R1 and R2 having same current and same number of turns,where B1 and B2 are the magnetic fields at their centres.
- The magnetic field at a point outside a thick straight wire carrying current is inversely proportional to the distance but magnetic field at a point inside the wire is directly proportional to the distance.

- If in a coil the current is clockwise, it acts as a South-pole. If the current is anticlockwise, it acts as North-pole.

- No magnetic field occurs at point P, Q and R due to a thin current element .

- Magnetic field intensity in a thick current carrying conductor at any point x is

- Graph of magnetic field B versus x

- Magnetic field is zero at all points inside a current carrying hollow conductor.

### MAGNITUDE AND DIRECTION OF MAGNETIC FIELD DUE TO DIFFERENT CONFIGURATION OF CURRENT CARRYING CONDUCTOR

### FORCE ON A CONDUCTOR

where,

α is the angle which the conductor makes with the direction of the field.

### TORQUE ON A COIL

### FORCE ACTING ON A CHARGED PARTICLE MOVING IN A UNIFORM MAGNETIC FIELD

### FORCE BETWEEN TWO PARALLEL CURRENTS

- No force acts on a charged particle if it enters a magnetic field in a direction parallel or antiparallel to the field.
- A finite force acts on a charged particle if it enters a uniform magnetic field in a direction with finite angle with the field.
- If two charged particles of masses m1and m2 and charges q1 and q2 are projected in a uniform magnetic field with same constant velocity in a direction perpendicular to the field then the ratio of their radii (R1: R2) is given by

- The force on a conductor carrying current in a magnetic field is directly proportional to the current, the length of conductor and the magnetic field.
- If the distance between the two parallel conductors is decreased (or increased) by k-times then the force between them increases (or decreases) k-times.
- The momentum of the charged particle moving along the direction of magnetic field does not change, since the force acting on it due to magnetic field is zero.
- Lorentz force between two charges q1 and q2 moving with velocity v1, v2 separated by distance r is given by

- If the charges move, the electric as well as magnetic fields are produced. In case the charges move with speeds comparable to the speed of light, magnetic and electric force between them would become comparable.
- A current carrying coil is in stable equilibrium if the magnetic dipole moment , is parallel to and is in unstable equilibrium when is antiparallel to .
- Magnetic moment is independent of the shape of the loop. It depends on the area of the loop.
- A straight conductor and a conductor of any shape in the same plane and between the same two end points carrying equal current in the same direction, when placed in the same magnetic field experience the same force.
- There is net repulsion between two similar charges moving parallel to each other in spite of attractive magnetic force between them. This is because of electric force of repulsion which is much more stronger than the magnetic force.
- The speed of the charged particle can only be changed by an electric force.

### MOVING COIL GALVANOMETER

### HALL EFFECT

- Determine the sign of charge carriers inside the conductor.
- Calculate the number of charge carriers per unit volume.