Flux Density due to a current flowing in a long
straight wire
© David Hoult 2009
© David Hoult 2009
© David Hoult 2009
The field at point p is directed
© David Hoult 2009
The field at point p is directed out of the plane of
the diagram (“corkscrew rule”)
© David Hoult 2009
© David Hoult 2009
The magnitude of B at
point p depends on
© David Hoult 2009
The magnitude of B at
point p depends on
the current, I
© David Hoult 2009
The magnitude of B at
point p depends on
the current, I
the perpendicular distance
of p from the wire
© David Hoult 2009
The magnitude of B at
point p depends on
the current, I
the perpendicular distance
of p from the wire
the medium surrounding
the wire
© David Hoult 2009
Experiments show that
BaI
and if r is small compared with the length of the
wire then
© David Hoult 2009
Experiments show that
BaI
and if r is small compared with the length of the
wire then
Ba 1
r
Therefore
© David Hoult 2009
Experiments show that
BaI
and if r is small compared with the length of the
wire then
Ba 1
r
Therefore
B = (a constant)
I
r
© David Hoult 2009
Because this is a situation having cylindrical
symmetry, the factor 2p is included in the equation
© David Hoult 2009
Because this is a situation having cylindrical
symmetry, the factor 2p is included in the equation
µI
B=
2pr
© David Hoult 2009
Because this is a situation having cylindrical
symmetry, the factor 2p is included in the equation
µI
B=
2pr
where µ is the permeability of the medium
surrounding the wire
© David Hoult 2009
Because this is a situation having cylindrical
symmetry, the factor 2p is included in the equation
µI
B=
2pr
where µ is the permeability of the medium
surrounding the wire
If the medium is a vacuum (or air) the permeability
is written as µo
© David Hoult 2009
Because this is a situation having cylindrical
symmetry, the factor 2p is included in the equation
µI
B=
2pr
where µ is the permeability of the medium
surrounding the wire
If the medium is a vacuum (or air) the permeability
is written as µo
The units of µ are
© David Hoult 2009
Because this is a situation having cylindrical
symmetry, the factor 2p is included in the equation
µI
B=
2pr
where µ is the permeability of the medium
surrounding the wire
If the medium is a vacuum (or air) the permeability
is written as µo
The units of µ are T A-1 m-1 =
© David Hoult 2009
Because this is a situation having cylindrical
symmetry, the factor 2p is included in the equation
µI
B=
2pr
where µ is the permeability of the medium
surrounding the wire
If the medium is a vacuum (or air) the permeability
is written as µo
The units of µ are T A-1 m-1 = NA-2
© David Hoult 2009
Because this is a situation having cylindrical
symmetry, the factor 2p is included in the equation
µI
B=
2pr
where µ is the permeability of the medium
surrounding the wire
If the medium is a vacuum (or air) the permeability
is written as µo
The units of µ are T A-1 m-1 = NA-2
1 N A-2 = 1 Henry per meter (H m-1)
© David Hoult 2009
Force acting between two long, parallel, currentcarrying conductors
© David Hoult 2009
© David Hoult 2009
© David Hoult 2009
© David Hoult 2009
© David Hoult 2009
Current I2 flows
through the field
produced by current I1
(and vice versa)
© David Hoult 2009
Current I2 flows
through the field
produced by current I1
(and vice versa)
Flux density near conductor 2 produced by I1 is
given by
© David Hoult 2009
Current I2 flows
through the field
produced by current I1
(and vice versa)
Flux density near conductor 2 produced by I1 is
given by
µo I1
B=
2pr
assuming that the medium is a vacuum (or air)
© David Hoult 2009
Force acting on a length L of wire 2 is
F = I2 L B
© David Hoult 2009
Force acting on a length L of wire 2 is
F = I2 L B
Therefore, force per unit length acting on wire 2 is
© David Hoult 2009
Force acting on a length L of wire 2 is
F = I2 L B
Therefore, force per unit length acting on wire 2 is
µo I1 I2
F
=
L
2pr
© David Hoult 2009
µo I1 I2
F
=
L
2pr
1 A is the current which,
© David Hoult 2009
µo I1 I2
F
=
L
2pr
1 A is the current which, when flowing in each of
two infinitely long, straight, parallel conductors,
© David Hoult 2009
µo I1 I2
F
=
L
2pr
1 A is the current which, when flowing in each of
two infinitely long, straight, parallel conductors,
separated by 1m,
© David Hoult 2009
µo I1 I2
F
=
L
2pr
1 A is the current which, when flowing in each of
two infinitely long, straight, parallel conductors,
separated by 1m, in a vacuum,
© David Hoult 2009
µo I1 I2
F
=
L
2pr
1 A is the current which, when flowing in each of
two infinitely long, straight, parallel conductors,
separated by 1m, in a vacuum, produces a force
per unit length of 2 × 10-7 N m-1
© David Hoult 2009
µo I1 I2
F
=
L
2pr
1 A is the current which, when flowing in each of
two infinitely long, straight, parallel conductors,
separated by 1m, in a vacuum, produces a force
per unit length of 2 × 10-7 N m-1
© David Hoult 2009
Flux density produced by a long coil (solenoid)
Current flowing through a conductor produces a
magnetic field. If the conductor is a long straight
wire, then the field is distributed over a large
region of space. If the wire is used to make a coil,
the magnetic field is concentrated into a smaller
space and is therefore stronger
© David Hoult 2009
The flux density, Bc at the centre of a long coil,
having N turns and of length L depends on
© David Hoult 2009
The flux density, Bc at the centre of a long coil,
having N turns and of length L depends on
the current flowing through the solenoid, I
© David Hoult 2009
The flux density, Bc at the centre of a long coil,
having N turns and of length L depends on
the current flowing through the solenoid, I
the number of turns per unit length
© David Hoult 2009
The flux density, Bc at the centre of a long coil,
having N turns and of length L depends on
the current flowing through the solenoid, I
the number of turns per unit length
the permeability of the medium inside the solenoid
© David Hoult 2009
Experiments show that the flux density, Bc on the
axis, at the centre of a solenoid is
directly proportional to I
directly proportional to N/L
© David Hoult 2009
Bc a I N
L
© David Hoult 2009
Bc a I N
L
The constant of proportionality is µ (the
permeability of the medium), therefore we have
© David Hoult 2009
Bc a I N
L
The constant of proportionality is µ (the
permeability of the medium), therefore we have
Bc = µ I N
L
© David Hoult 2009
The flux density on the axis at the end of the
solenoid is equal to
© David Hoult 2009
The flux density on the axis at the end of the
solenoid is equal to Bc / 2
© David Hoult 2009
The flux density on the axis at the end of the
solenoid is equal to Bc / 2
© David Hoult 2009
The flux density on the axis at the end of the
solenoid is equal to Bc / 2
© David Hoult 2009
© David Hoult 2009