King Saud University
College of Applied Studies
and Community Service
Department of Natural Sciences
Magnetic Filed due to Electric
Current
General Physics II
PHYS 111
Nouf Alkathran
Outline
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Magnetic Field
Monopoles
Unit of Magnetic Field
Oersted’s experiment
Characteristics of Magnetic Lines
Magnetic Force on a Point Charge
Electromagnetic induction
The Right Hand Rule
Magnetic Field around Current Carrying Wire
Outline
• Magnetic Field due to a Current Carrying Circular
Loop
• Magnetic Field Produced by a Current-Carrying
Solenoid
• Ideal Solenoid – Characteristics
• Magnetic Force on a Current-Carrying Conductor
• Direction of Magnetic Force on a Current-Carrying
Conductor
• Magnetic Flux
Outline
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Magnetic Flux Through a Plane, 1
Magnetic Flux Through a Plane, 2
Faraday’s Law
Fleming's Right and Left Hand Rules
Questions
Magnetic Field
• A charged object produces an
electric field E at all points in
space. In a similar manner, a bar
magnet is a source of a magnetic
field B.
• The region around a magnet
where the force of attraction or
repulsion can be detected is called
Magnetic Field.
• A bar magnet consists of two
poles, which are designated as
• the north (N)
• the south (S)
Magne?c field produced by a bar magnet.
Magnetic Field
• The magnetic field lines leave from the north pole
and enter the south pole.
• When holding two bar magnets close to each other,
the like poles will repel each other while the opposite
poles attract
Monopoles
• Unlike electric charges, which can be isolated,
the two magnetic poles always come in a pair.
When you break the bar magnet, two new bar
magnets are obtained, each with a north pole
and a south pole “monopoles”
Magne?c monopoles do not exist in isola?on
Unit of Magnetic Field
• The SI unit for magnetic field is the Tesla,
which can be seen from the magnetic part of
the Lorentz force law Fmagnetic = qvB to be
composed of (Newton x second)/(Coulomb x
meter).
Oersted’s experiment
• in 1820, Oersted ran
experiments with
conducting wires run near a
sensitive compass. The
orientation of the wire and
the direction of the flow
both moved the compass
needle.
Oersted’s experiment
CHARACTERISTICS OF
MAGNETIC LINES
• Magnetic lines of force
start from the North
Pole and end at the
South Pole.
• Two magnetic lines of
force can not intersect
each other.
• Magnetic fields are
strongest at the poles.
Magnetic Force on a Point Charge
• The magnetic force on a point charge is:
F =q(v×B)
• The unit of magnetic field (B) is the tesla (1T
= 1 N/Am).
• A further unit for the magnetic field is gauss:
1G = 10-4 T.
• The magnitude of FB is: F =qB(vsinθ)
Magnetic Force on a Point Charge
• where vsinθ is the component of the velocity
perpendicular to the direction of the magnetic
field. θ represents the angle between v and B.
• The direction of FB is found from the righthand rule.
• For a general cross product: C = A×B
Note: C=A×B≠B×A
The Right Hand Rule
1. The thumb is in the
direction of the
current.
2. The direction of the
field is the same as the
direction of the
fingers.
Magnetic Field around Current
Carrying Wire
• The magnetic field lines around a straight
current carrying wire are a set of concentric
circles around the wire, running the length
of the wire. The direction of the field is
based on the right hand rule.
Magne?c Field around Current Carrying Wire
Magnetic Field around Current
Carrying Wire
• The strength of the field (B) can be given by
Where :
I is the current in the wire,
is a constant known as the permeability of free
space.
r is the radial distance from the wire.
Magnetic Field due to a Current
Carrying Circular Loop
• The lines near the
centre of the loop are
almost straight. The
magnetic field at the
centre of the loop is
perpendicular to the
plane of the loop.
Magnetic Field due to a Current
Carrying Circular Loop
• If circular loop of radius a carries a current I ,
then the the magnetic field at the center of the
loop given by:
Where:
a radius of the loop
I current
is a constant known as the permeability of free
space.
Magnetic Field Produced by a
Current-Carrying Solenoid
• A solenoid is a long coil of wire (with many turns
or loops). Because of its shape, the field inside a
solenoid can be very uniform, and also very
strong.
Magnetic Field Produced by a
Current-Carrying Solenoid
• The field just outside the coils is nearly zero.
• The magnetic field inside of a current-carrying
solenoid is very uniform in direction and
magnitude. Only near the ends does it begin to
weaken and change direction.
Magnetic Field Produced by a
Current-Carrying Solenoid
• The magnetic field strength inside a solenoid is
simply
B=µ 0nI (inside a solenoid),
Where
N is the number of loops per unit length of the
solenoid (n=N/L, with N being the number of
loops and L the length).
• This is valid only at points near the center of a
very long solenoid.
Magnetic Field of a Tightly Wound
Solenoid
•The field distribution is
similar to that of a bar
magnet.
•As the length of the
solenoid increases,
– The interior field
becomes more
uniform.
– The exterior field
becomes weaker.
Ideal Solenoid – Characteristics
•An ideal solenoid is
approached when:
– The turns are closely
spaced.
– The length is much greater
than the radius of the turns.
Magnetic Force on a CurrentCarrying Conductor
• When an electrical wire is exposed to a
magnet, the current in that wire will be
affected by a magnetic field. The effect comes
in the form of a force.
• The expression for magnetic force on current
can be found by summing the magnetic force
on each of the many individual charges that
comprise the current.
Magnetic Force on a CurrentCarrying Conductor
• The force (F) a magnetic field (B) exerts on an
individual charge (q) traveling at drift velocity Vd:
F=qvdB sinθ
the total magnetic force on the wire is:
F=NqvdBsinθ
Given that N=nV, where n is the number of charge
carriers per unit volume and V is volume of the wire, and
that this volume is calculated as the product of the circular
cross-sectional area A and length (V=Al)
F=(nqAvd)lBsinθ.
Magnetic Force on a CurrentCarrying Conductor
• The terms in parentheses are equal to current
(I), and thus the equation can be rewritten as:
F=IlB sinθ
Direction of Magnetic Force on a
Current-Carrying Conductor
• The direction of the magnetic
force can be determined using the
right hand rule, demonstrated in .
The thumb is pointing in the
direction of the current, with the
four other fingers parallel to the
magnetic field. Curling the
fingers reveals the direction of
magnetic force.
Fleming 's left-hand rule
• Hold the fore finger, the
center finger and the thumb
of left hand at right angles
to one another. Adjust
fingers in such a way that
the forefinger points in the
direction of magnetic field
and center finger points in
the direction of current,
then the direction in which
the thumb points,gives the
direction of force acting on
the conductor.
Magnetic Flux
•The magnetic flux associated
with a magnetic field is defined
in a way similar to electric flux.
•Consider an area element dA on
an arbitrarily shaped surface.
•The magnetic field in this B
element is .
• dA is a vector that is
perpendicular to the surface and
has a magnitude equal to the area
dA.
Magnetic Flux
•The magnetic flux ΦB is
! !
B  B d A
= B = BAcos 
Where
A is the area – for circular loop A= π r2
B is the magnetic field
•The unit of magnetic flux is T.m2 = Wb
– Wb is a weber
Magnetic Flux Through a
Plane, 1
•A special case is when a plane
of area A makes an angle θ
with dA.
•The magnetic flux is ΦB = BA
cos θ.
•In this case, the field is parallel
to the plane and ΦB = 0.
Magnetic Flux Through A
Plane, 2
•The magnetic flux is
B = BAcos 
•In this case, the field is
perpendicular to the plane and
B = BA.
•This is the maximum value of
the flux.
Electromagnetic induction
• Electromagnetic induction (or sometimes just
induction) is a process where a conductor placed in a
changing magnetic field (or a conductor moving
through a stationary magnetic field) causes the
production of a voltage across the conductor. This
process of electromagnetic induction, in turn, causes an
electrical current - it is said to induce the current.
Electromagnetic induction
• Faraday discovered that a voltage would be generated
across a length of wire if that wire was exposed to a
perpendicular magnetic field flux of changing intensity.
Electromagnetic induction
1. Motion of a magnet with respect
to a coil produces induced
current
• An easy way to create a magnetic
field of changing intensity is to
move a permanent magnet next to a
wire or coil of wire.
• If a magnet is moved towards or
away from a coil of wire connecting
to galvanometer needle shows a
deflection. This shows that current is
induced in the coil due to the motion
of magnet.
Electromagnetic induction
2. Changing in magnetic field
produces induced current
• take two coils of wires wound
around a cylindrical paper roll.
Connect one coil to a battery and
the other coil to a galvanometer.
If current is passed through the
first coil, the galvanometer
needle shows a deflection in the
second coil . If the current is
disconnected , the needle moves
in opposite direction. This shows
that current is induced due to
change in magnetic field.
Faraday’s Law
• Faraday was able to mathematically relate the rate of change of
the magnetic field flux with induced voltage :
• The current is given by I=e/ R
Where
E is induced volltage
R is resistance
Electromagnetic induction
• A magnetic field of changing intensity perpendicular to
a wire will induce a voltage along the length of that
wire. The amount of voltage induced depends on the
rate of change of the magnetic field flux and the
number of turns of wire (if coiled) exposed to the
change in flux.
• Faraday's equation for induced voltage: e = N(dΦ/dt)
• A current-carrying wire will experience an induced
voltage along its length if the current changes (thus
changing the magnetic field flux perpendicular to the
wire, thus inducing voltage according to Faraday's
formula)
Fleming's right hand rule
• the thumb,the fore finger and
the center finger of right
hand at right angles to one
another. Adjust fingers in Magne$c field B
such a way that forefinger
points in the direction of
Induced current I
magnetic field, the thumb
points in the direction of
motion of conductor,then the
direction in which center
finger points,gives the
direction of induced current
in the conductor.
Mo$on or force F
Fleming's Right and Left Hand Rules
• Left hand rule determines the direction of force
acting on a current carrying wire placed in a
magnetic field.
• whereas right hand rule gives the direction of
induced current produced in a straight
conductor moving in a magnetic field.
Questions
• Find the direction of magnetic field at point x
where the arrow shows the current in the wire.
a)
b)
c)
d)
Into the page
Out of the page
Up
down
Questions
• What are the effects of moving a closed wire
loop through a magnetic field?
A. A voltage is induced in the wire.
B. A current is induced in the wire.
C. All of the above
Questions
• The unit of flux density is known as
A. magnetomotive force
B. a weber
C. a maxwell
D. a tesla
Questions
• The electromotive force is created by the
change in
A. magnetic field
B. universal force field
C. electric field
D. gravitational field
Questions
• A circular loop of radius 0.10 m is rotating in
a uniform magnetic field of 0.20 T. Find the
magnetic flux through the loop when the plane
of the loop and the magnetic field vector are
parallel.
a. Zero
b. 3.1X10-3 Tm2
c. 5.5X10-3 Tm2
d. 6.3X10-3 Tm2
Questions
• A magnetic field of strength 0.30 T is directed
perpendicular to a plane circular loop of wire
of radius 25 cm. Find the magnetic flux
through the area enclosed by this loop.