Question
Question: The correct relation between.\(B,H\text{ and }I\).is \(\begin{aligned} & \text{A}\text{. }B={{...
The correct relation between.B,H and I.is
A. B=μ0I×HB. B=Hμ0IC. B=μ0(I+H)D. B=μ0I−H
Solution
B represents the magnetic induction, H represents the magnetizing field intensity, and I represents the intensity of magnetization, for a given system. I is also represented as M. They are all interrelated to each other. Write the expression for each of them and do some substitution to get the relationship between B,H and I.
Formula used:
B=μ0niH=niM or I=Volumemagnetic moment developedMagnetic moment developed, m= pole strength developed×distance between the poles
Where,
μ0=permeabilityn=number or rotation of a solenoid.i= current through the solenoid.
Complete step by step answer:
Magnetic induction (B): When current flows inside the wire of a solenoid some magnetic moments developed. This current i induces some magnetic field inside solenoid called magnetic induction and is given by B=μ0ni, where n= number of turns of solenoid.
Magnetizing field intensity (H): The ability of the magnetizing field to magnetize a material medium is called magnetic field intensity. Its magnitude is defined as the number of turns of solenoid per unit length required to produce a given magnetic field,
So H=ni, but B0=μ0ni=μ0H
The intensity of magnetization (I).When a magnetic material is placed in the magnetizing field it gets magnetized. The magnetic moment developed per unit volume of the material is called intensity of magnetization, thus M=Vm
If magnetic induction Bm produced due to magnetizing field then magnetic field intensity.
I=μ0M
As the total magnetic field or the magnetic induction Binside a magnetic material is the resultant of magnetizing field Boand the field Bmproduced due to magnetization of the material. So
B=B0+Bm=μ0H+μ0I⇒B=μ0(H+I)
Hence, the correct answer is option C.
Note:
Note that the S.I unit of magnetic induction is tesla(T) or weber×meter−2(Wbm−2) which is equivalent to Nm−1A−1 or JouleA−1m−2. And the S.I unit of Magnetizing field intensity is
Ampere×meterr−1 which is equivalent to m2TN or Weber×meterJoule.