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Electricity and Magnetism: Magnetic force, field, and electromagnetic induction
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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