Magnetic Fields and Current-Carrying Wires

• Magnetic fields are created where current exists.

Magnetic Fields and Straight Wires

• A magnetic field occurs around a current-carrying wire.
• The field lines are circular, with their direction dependent on the current's direction.
• This magnetic field only lasts as long as the current flows through the wire.

Determining Magnetic Field Direction

• Use the right-hand rule; grasp the wire with your right hand, thumb pointing in the direction of the current, and your fingers will curl in the direction of the magnetic field.
• Magnetic field lines go from North to South outside a magnet and South to North inside the magnet.
• Magnetic field lines are unidirectional and never cross each other.
• Stronger magnetic fields have field lines closer together (near poles), while weaker fields have field lines farther apart.

Magnetic Fields and Force

• The direction of the magnetic field at any point can be found by drawing a tangent at that point.
• Magnetic field lines are imaginary.
• Like poles repel, and opposite poles attract.
• Force on a current-carrying conductor is given by F = ILBsin(θ).
• Use the right-hand rule to determine the force direction; point your middle finger in the direction of the magnetic field, your thumb in the direction of the current, and the force will be normal to the palm.

Force, Fields, and Conductors

• Force is directly proportional to sin(θ), where θ is the angle between the conductor and the field.
• Force is directly related to current and length of the conductor.
• Force is directly related to magnetic field strength F α ILBsin θ.

Magnetic Induction

• Magnetic field strength (B), also known as magnetic induction, is defined as the force acting on one meter length of the conductor placed at a right angle to the magnetic field when 1A current is passing through it.
• The SI unit for B is Tesla (T).
• A more practical unit is the gauss (G).
• 1 Tesla (T) = 10^4 gauss (G).
• Magnetic field originates out of the plane of paper.

Parallel Conductors

• If two parallel conductors have current passing through them in the same direction, their magnetic fields interact and attract each other.
• If the current runs in opposite directions, they repel each other.
• Magnetic field strength is medium-dependent.

Magnetic Flux and Density

• Magnetic flux density is the change in flux per unit area.

Magnetic Field Factors

• The magnetic field is directly proportional to the current's magnitude.
• Stronger currents lead to stronger magnetic fields around the conductor.
• Inversely proportional to the conductor's length
• Magnetic field is inversely proportional to the distance from the wire.

Ampere's Law

• Ampere's law is used to find magnetic field intensity.
• For any closed path, the dot product of the magnetic field (B) and length element (Δl) equals μ₀ times the total current enclosed by the loop μ₀ is a constant related to the medium, called the permeability of free space, and its value in free space is 4π x 10⁻⁷ Wb/A.m.

Applications of Amperes Law

• A straight current-carrying wire.
• When current passes through a solenoid, a magnetic field similar to that of a bar magnet is created.
• The field inside the solenoid is strong and uniform.

Moving Charges and Magnetic Fields

• The relative permeability of the core material and the force on a moving charge in a uniform magnetic field follows F = qvBsin Θ

Calculating e/m

• The value can be calculated using beams of charged particles in a uniform magnetic field
• Uniform magnetic field B, will experience a force of F = q(v x B) and will start moving in a circular trajectory of radius r.

Cathode Ray Oscilloscope (CRO)

CROs works by deflecting a beam of electrons as they pass through uniform electric field between two sets of parallel plates.

• Anodes accelerate the electronic beam to a fixed spot on a fluorescent screen.
• Deflection plates deflect the beam
• CROs need a waveform that is a saw tooth voltage of period T

CRO Waveforms

• If a sinusoidal voltage is applied across the y-plates simultaneously with a time base voltage impressed across the x-plates
• A sinusoidal wave which itself gives rise to a vertical line, will now spread out & will appear as a sinusoidal trace on the screen

Galvanometers

• Torque (T) = (Force) x (moment arm)
• T = BIA cos Q if the coil makes an angle
• where Q is the Field Direction

Galvanometer Torque

• Torque is enhanced: T=BIAN Cos(Q).
• The equation for torque is valid for circular coils and radial fields.

Galvanometer Sensitivity

A Galvanometer: a single simple instrument in which a coil isis suspended by a strip along its axis of rotation in a magnetic field.

• A pointer which can move over a scale..
• The pointer moves on the scale showing whether current is small or large depending on the size of the deflection.
• Attached to the strip is a spring.

Current Flow in a Galvanometer

• Effect of the field due to the current and magnetic field B, a torque is produced
• Is measured with formulas that depend on number of windings, magnetic field, current

Current Sensitivity

• Defined by the current in microamperes required to produce 1mm deflection on a scale placed 1m from the mirror of Galvanometer.
• To make the Galvanometer more sensitive: make B, A,N or increase the number of windings

Electrical Devices

• A galvanometer is a part of each device
• Voltmeter: It must have a very high resistance, so that it will not short the circuit across which the voltage