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, Ithe perpendicular distance of p from the wire David Hoult 2009

The magnitude of B at point p depends on the current, Ithe perpendicular distance of p from the wirethe medium surrounding the wire David Hoult 2009

Experiments show thatB a Iand if r is small compared with the length of the wire then David Hoult 2009

and if r is small compared with the length of the wire then Experiments show thatThereforeB a IB a1r David Hoult 2009

B a Iand if r is small compared with the length of the wire then Experiments show thatB a1rThereforeB =Ir(a constant) 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 equationB = I2 p r David Hoult 2009

Because this is a situation having cylindrical symmetry, the factor 2p is included in the equationB = I2 p rwhere 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 equationB = I2 p rwhere is the permeability of the medium surrounding the wireIf the medium is a vacuum (or air) the permeability is written as o David Hoult 2009

Because this is a situation having cylindrical symmetry, the factor 2p is included in the equationB = I2 p rwhere is the permeability of the medium surrounding the wireIf the medium is a vacuum (or air) the permeability is written as oThe units of are David Hoult 2009

Because this is a situation having cylindrical symmetry, the factor 2p is included in the equationB = I2 p rwhere is the permeability of the medium surrounding the wireIf the medium is a vacuum (or air) the permeability is written as oThe units of are T A-1 m-1 = David Hoult 2009

Because this is a situation having cylindrical symmetry, the factor 2p is included in the equationB = I2 p rwhere is the permeability of the medium surrounding the wireIf the medium is a vacuum (or air) the permeability is written as oThe units of 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 equationB = I2 p rwhere is the permeability of the medium surrounding the wireIf the medium is a vacuum (or air) the permeability is written as oThe units of are T A-1 m-1 = NA-21 N A-2 = 1 Henry per meter (H m-1) David Hoult 2009

Force acting between two long, parallel, current-carrying 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)B =o I12 p rFlux density near conductor 2 produced by I1 is given byassuming that the medium is a vacuum (or air) David Hoult 2009

Force acting on a length L of wire 2 isF = I2 L B David Hoult 2009

Force acting on a length L of wire 2 isF = I2 L BTherefore, force per unit length acting on wire 2 is David Hoult 2009

Force acting on a length L of wire 2 isF = I2 L BTherefore, force per unit length acting on wire 2 iso I1 I22 p rFL= David Hoult 2009

o I1 I22 p rFL=1 A is the current which, David Hoult 2009

o I1 I22 p rFL=1 A is the current which, when flowing in each of two infinitely long, straight, parallel conductors, David Hoult 2009

o I1 I22 p rFL=1 A is the current which, when flowing in each of two infinitely long, straight, parallel conductors, separated by 1m, David Hoult 2009

o I1 I22 p rFL=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

o I1 I22 p rFL=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

o I1 I22 p rFL=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 current flowing through the solenoid, IThe flux density, Bc at the centre of a long coil, having N turns and of length L depends on David Hoult 2009

the current flowing through the solenoid, IThe flux density, Bc at the centre of a long coil, having N turns and of length L depends onthe number of turns per unit length David Hoult 2009

the current flowing through the solenoid, IThe flux density, Bc at the centre of a long coil, having N turns and of length L depends onthe number of turns per unit lengththe 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 Idirectly 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 (the permeability of the medium), therefore we have David Hoult 2009

Bc a I N L The constant of proportionality is (the permeability of the medium), therefore we haveBc = 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