Magnetism; MF lines and Magnetic flux; motion of charged particles; MF on current-carrying loops; Applications; DC motors

Magnetic Fields and Magnetic Forces

Magnetism

• The fundamental nature of magnetism is the interaction of moving electric charges.

Magnetism

• Electric forces may act on charges whether they are at rest or moving.• Magnetic forces act

only on moving charges.

Magnetism• It’s N geographic

pole is close to a magnetic S-pole.

• Magnetic declination or magnetic variation is observed.

Magnetism

• No single isolated magnetic pole exists.• Poles always

appear in pairs.

• First to discover the relationship of magnetism to moving charges

• A compass needle was deflected by a current-carrying wire

Hans Christian Oersted

• Discovered that moving a magnet near a conducting loop can cause a current in the loop.

Michael Faraday and Joseph Henry

Magnetic Field and Force

• A moving charge or a current creates a magnetic field in the surrounding space.

• The magnetic field exerts a force on any other moving charge or current that is present in the field.

Magnetic Field and ForceAt any position, the direction of B is defined as that which the N-pole of a compass needle tends to point.

Magnetic field (B) is a vector field.

F is always perpendicular to B and v.

The magnitude of a magnetic force also depends on the particle’s velocity.

The magnitude of a magnetic force is proportional to the magnitude of the field.

The magnitude of a magnetic force is proportional to the magnitude of the charge.

Magnetic Field and Force

Coulomb’s Law for Magnetism

Where m is magnetic pole strength; k= 10-7N.m2/(Amp.m)2

d = distance

F = k(m1m2/d2)

Draw vectors v and B with their

tails together.

Imagine turning v until it points in

the direction of B.

Your thumb then points in the direction of F.

F = qv x BF = qvBsinɸ

Magnetic Field and Force

• Find the forces exerted by the N poles of the magnets to each other.

Example

4.10x10-14N

A beam of protons (q=1.6x10-19C) moves at 3.0x105m/s through a uniform magnetic field with magnitude 2.0T that is directed along the positive z-axis. The velocity of each proton lies in the xz-plane at an angle of 30° to the +z-axis. Find the force on a proton.

Example

4.8x10-14N

Magnetism

What is the direction of the magnetic force on the

charge?

Field lines• The idea is the same

for the electric field lines.

• When adjacent field lines are close together, the field magnitude is large.

Magnetic flux ΦB

• Same idea as the electric flux: The net magnetic flux through the surface of an enclosed area is directly proportional to the magnitude of the net charge enclosed

Magnetic Field Lines and Flux

Magnetic Flux

B

B

Magnetic Flux

ΦB = BAcosɸ

Where B is magnetic field; A is area vector

Magnetic Flux

• SI unit is weber (Wb)• B may also be called

magnetic flux density.• The total magnetic

flux through a closed surface is always zero.

B

A flat surface has an area of 3.0 cm2 in a uniform magnetic field. If the magnetic flux through this area is 0.90 mWb, calculate the magnitude of the magnetic field and find the direction of the area vector.

Example

B = 6.0 TArea vector = perpendicular

Motion of Charged particles in a Magnetic field

• Motion of a charged particle under the action of a magnetic field alone is always motion with constant speed.

Motion of Charged particles in a Magnetic field

ac = v2 / R

Where v is velocity; R is radius

Motion of Charged particles in a Magnetic field

F = qvB = mv2 / R

Where q is charge R is radius m is mass

Motion of Charged particles in a Magnetic field

ω= v/R = qB/m = 2πf

Where q is charge, R is radius, m is mass, f is frequency

• A magnetron in a microwave oven emits electromagnetic waves with frequency 2450 MHz. What magnetic field strength is required for electrons to move in a circular path with this frequency?

• m= 9.11x10-31kg; q= 1.60x10-19C

Example

B = 0.0877 T

Applications of Motions of Charged Particles

Velocity selector

Magnetic Forceon a Current Carrying Conductor

The force is always perpendicular to both the conductor and field

Magnetic Forceon a Current Carrying Conductor

F = qvd x B = qvdB sinɸ

Where F = force; vd = drift velocity;

B = magnetic field

Magnetic Forceon a Current Carrying Conductor

F = I l x B = IlB sinɸ

Where F = force; I = current; l = length; B = magnetic field

Magnetism

Example

A straight horizontal copper rod carries a current of 50.0 A from west to east in a region between the poles of a large electromagnet. In these region, there is a horizontal magnetic field toward the northeast (45° N of E) with magnitude 1.20 T.

A. Find the magnitude of the force on a 1.00 m section of rod.B. While keeping the rod horizontal, how should it be oriented to maximize the magnitude of force?

MagnetismExample

A. 42.4 NB. Perpendicular (F=60.0 N)

Force and Torqueon a Current Carrying Loop

•The net force on a current loop in a uniform magnetic field is zero.

•However, the net torque is not, in general, equal to zero.

Force and Torqueon a Current Carrying Loop

τ = IBA sin ɸ

μ = IA

τ = μB sin ɸ = μ x B

Magnetism

a

bµ

B

I

Example

A circular coil 0.0500 m in radius lies in a horizontal plane. It carries a current of 5.00 A in a counter-clockwise sense when viewed from above. The coil is in uniform magnetic field directed toward the right with magnitude 1.20 T. Find the magnitudes of the magnetic moment and the torque on the coil.

Example

A circular coil 0.0500 m in radius with 30 turns of wire lies in a horizontal plane. It carries a current of 5.00 A in a counter-clockwise sense when viewed from above. The coil is in uniform magnetic field directed toward the right with magnitude 1.20 T. Find the magnitudes of the magnetic moment and the torque on the coil.

Example

μ = 3.93 x 10-2 Am2 ; μtotal = 1.18 Am2 ;

τ = 0.0471 Nm τtotal = 1.41 Nm

The Direct-Current Motor

In a motor:• The magnetic

torque acts on a current-carrying conductor

• Electric energy is converted to mechanical energy

The Direct-Current Motor

The Direct-Current Motor

Rotor• Is the moving part of

the motor• It is a loop of wire

formed into an open ended loop and free to rotate about an axis

The Direct-Current Motor

The Direct-Current Motor

Commutator• Formed by the

attachment of the rotor wires to circular conducting segments

The Direct-Current Motor

The Direct-Current Motor

Brushes• makes contact with

the each commutator segment

• are parts of an external circuit that includes a source of emf

The Direct-Current Motor

The Direct-Current MotorThe Direct-Current Motor

MagnetismThe Direct-Current Motor

Vab= Ԑ + Ir

Where Vab = voltage; Ԑ = electromotive force;

I = current;r = internal resistance

MagnetismThe Direct-Current Motor

P = VabI= I2R

Where Vab = voltage; I = current;R= resistance

Magnetism• A dc motor with its rotor and field coils

connected in series has an internal resistance of 2.00Ω. When running at full load on a 120-V line, it draws a current of 4.00A.

a) What is the emf in the rotor?

b) What is the power delivered to the motor?

c) What is the rate of dissipation of energy in the resistance of the motor?

Example

Magnetism

a) ԑ=112Vb)P input= 480W

c) P dissipated= 32W

Source: Young, Hugh D., and Freedman, Roger A. 2002, Reprinted. University Physics with Modern Physics. 10th ed. Singapore: Pearson Education Asia Pte Ltd. Copyright ©

2000 by Addison-Wesley Publishing Longman, Inc.

PowerPoint edited by Mr. Jon Sithli Mendoza