# Why aren't magnetic fields affected when a conductor is placed in the field?

For electric fields when a conductor such as an aluminium sheet is placed in the field the field lines get affected due to the conductor.But when a conductor is placed in a magnetic field there will be no change in the magnetic field lines.For example if there are two parallel wires carrying an electric current in the same direction they will experience a force due to the magnetic filed generated. If we insert a conductor between the two wires(aluminium sheet) still the two wires would experience the same force. Why isn't the field affected by the conductor?

• The field is affected by the conductor. See my answer and comment to a different answer below. – freecharly Oct 23 '16 at 16:57
• Yes i think with the addition of that comment the answer is complete now. – VJay Oct 24 '16 at 15:33

Instead of speaking the effect of magnetic (or electric) field lines when a conductor is placed near it , it is better to speak the other way round. The electric field lines get distorted in the presence of a conductor, because the electric field could could induce some charge on the conductor and hence the electric field due to that conductor opposes the external field lines. That's why the structure of field lines change.

A magnetic field affect only charged particles in motion. The equation for magnetic force is given by:

$$\vec{F}_{mag}=q\vec{v}\times\vec{B}$$

From this equation, it is clear that if the velocity of the charged particle in a magnetic field is zero, then it will experience no magnetic force.

In the case of conductor, even though there are free charges on it, they are in equilibrium and hence not affected by the magnetic field, since the net velocity vector of a charged particle is zero. But, if you place the conductor in a time-varying magnetic field, then the conductor experiences some force, which is due to the electric field generated by the time-varying magnetic field:

$$\frac{\partial\vec{B}}{\partial t}=-\nabla\times \vec{E}$$

What that happens between two current carrying wires is that the magnetic field of one is affecting the moving charges on the other. That's why the magnetic field lines are not affected by the conductor.

• This argumentation is not completely correct. If you insert a conductor into a magnetic field, the electrons experience the Lorentz force due to this conductor movement so that according to Lenz' law currents are induced causing a counteracting magnetic field trying to prevent the outer field penetration. Thus, in the first moment a magnetic field shielding does occur which, however, quickly disappears due to the resistive damping of the induced eddy currents. If the resistivity of the conductor is zero, the eddy currents would persist producing a perfect magnetic shield. – freecharly Oct 23 '16 at 16:50
• When the conductor just enters the field, of course induction occurs. However the question is not about a moving conductor in a magnetic field. It's about the presence of a conductor in a field. Also, since the charges are in equilibrium, a single magnetic field cannot affect the conductor charges, you need an electric field too as in the case of Hall effect. – UKH Oct 24 '16 at 0:17
• I have no quarrel for hat you have said. It's true. But here is what you should consider. From the question, it is clear that OP had an inference from the experiment and it's about why the field in the presence of a conductor. I have only answered the "no-affected" part only. – UKH Oct 24 '16 at 0:37
• I just wanted to show that when you consider the placement of the conductor as a time dependent process, there is, in general, a transient effect (shielding) on the magnetic field. When you consider a conductor with resistivity zero, there is even a permanent (stationary) shielding effect on the magnetic field. (See also Meissner effect.) Also, during the insertion of the conductor, there is no "equilibrium" and currents are induced by induced electric field in the frame of the conductor. – freecharly Oct 24 '16 at 0:45
• @Umnikrishnan - I understand your point... – freecharly Oct 24 '16 at 0:48

The magnetic field is affected when a conductor is placed in the field. The effect, however, depends on resistivity of the conductor and the time scale you are considering. If you insert a (not too thin) superconducting foil with resistivity zero between the wires, the magnetic field will be practically completely shielded because (eddy) currents are induced in the foil which counteract the magnetic field so that it cannot penetrate the foil. This shielding lasts as long as the foil is superconductive. Also in the aluminum foil with finite resistivity, during a very short time after a fast insertion, such eddy currents counteracting the penetration of the outside magnetic fields are induced but they quickly subside due to the dissipative loss damping of the currents in the foil.

Magnetic fields have two definitions. The first is the magnetic field $\vec B$ defined from the Lorentz force equation $\vec F~=~q\vec v\times \vec B$, which means the magnetic field has units $Ns/coul-m$ or $N/m-A$ for $A$ meaning ampere a unit of current. This unit is defined as a Tesla $T$. The flux of the magnetic field is a Weber $w~=~T/m^2$. This accompanies the $\vec H$ field that is defined according to a magnetic permeability $\mu$ which in free space is $\mu_0~=~3\pi\times 10^{-7}Vs/Am$ and we have $$\vec B~=~\mu\vec H.$$ This is analogous to the definition of the electric field $\vec E~=~\vec D/\epsilon$ according to the electric displacement vector and the dielectric constant.

Both of these can be used to describe the magnetization of a material. The magnetization field is $\vec M~=~\vec B/\mu_0~-~\vec H$. The magnetic field can now we see to depend on the magnetic permeability of the material. A large $\mu$ induces magnetic field lines to accumulate into the material. This is one reason that ferromagnetic materials are attracted to magnetic fields. Such materials have complex physics with charges, and Heisenberg showed quantum mechanically how atoms in such systems act as current loops with a magnetic field. An applied magnetic field induces a torque on these atomic current loops which in turn means the ferromagnetic material is under a magnetic force. These materials are usually conductors, though there are some materials with magnetization fields that are not conductors. There are also conductors that are not magnetic or ferrormagnetic such as aluminum.