# B field and H field confusion, physics GRE

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I'm getting ready for the exam that's coming up and I just took the 2017 practice exam to see what the last gaps are that I need to fill.

Question 96 of this exam asks: "The magnetic field inside a long coil of wire (solenoid) has a certain magnitude and direction when the coil is air filled. If a diamagnetic material is inserted in the coil, how do the magnitude and direction of the magnetic field change?"

A: Magnitude increases, direction is the same
B: Magnitude increases, direction is opposite
C: Magnitude decreases, direction is the same
D: Magnitude decreases, direction is opposite
E: Magnitude is unchanged, direction is opposite.

My (incorrect) reasoning was that since B = μH and μ increases while H is independent of the material, I assumed that the answer was A. This is incorrect, and the correct answer is C. My first mistake was to assume that "magnetic field" referred to B rather than to H, and second to assume that since the magnetic field is independent of the material, B would increase if μ increases.

As I now understand it, the correct reasoning would have been to recognize that inserting a diamagnetic core into a solenoid doesn't change the value of B within the solenoid, and therefore since μ has increased, H must decrease, and here "magnetic field" refers to H.

Anyway, the reason that I'm confused is that in my classes, B was often referred to as the "magnetic field", but apparently on the PGRE "magnetic field" means H.

So my question is: On the Physics GRE, if it asks me about the "magnetic field", does this always mean H?

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A diamagnetic material has $\mu_r <1$ where $\mu=\mu_r \mu_o$. The $H$ is the same in both cases and just depends upon the current in the windings of the solenoid. (Here we are using the definition that $B=\mu H$ ). $\\$ Meanwhile the magnetic field is $B$. The magnetic field $B$ has decreased with the diamagnetic material, because $\mu_r=1$ for air, and $\mu_r <1$ for the diamagnetic material.$\\$ In the pole model of magnetism, which is where $H$ gets its complete definition, $H$ is something of a construction that includes a contribution from currents in conductors plus a contribution from any poles. For a long cylinder, the pole contributions are minimal. $\\$ Additional item: In general $B=\mu_o H+\mu_o M$. For linear materials we can write $M=\chi_m H$, where $\chi_m$ is the magnetic susceptibility. For diamagnetic materials, $\chi_m<0$. The magnetism $M$ that results in diamagnetic materials points opposite the applied field $H$. It should be clear from this why $\mu_r<1$ for diamagnetic materials. (Without any significant poles in the problem, $H$ can be viewed as the applied field, particularly for the case of a long cylindrical sample inside a long solenoid). $\\$ (Note: In SI units, $B$ and $H$ are measured on a different scale, with $B=\mu_o H$ when $M=0$. In c.g.s. units, they use $B=H+4 \pi M$, so that $B$ and $H$ are on equal footing, rather than with a factor of $\mu_o=4 \pi \cdot 10^{-7}$ between them. In SI units, you can think of the applied magnetic field as being $\mu_oH$, to treat it equally with the magnetic field $B$ ). $\\$ Additional note: For paramagnetic materials, $M$ points along $H$, but $\mu_r$ is just slightly greater than 1. For ferromagnetic materials, $M$ points along $H$ as well, and $\mu_r$ can be 100 or even 1000 or greater. In general $\mu_r>>1$ for ferromagnetic materials.

Last edited:
jedishrfu
Mentor
Here's what wikipedia says:
The H-field
In addition to B, there is a quantity H, which is often called the magnetic field.[nb 3] In a vacuum, B and H are proportional to each other, with the multiplicative constant depending on the physical units. Inside a material they are different (see H and B inside and outside magnetic materials). The term "magnetic field" is historically reserved for H while using other terms for B. Informally, though, and formally for some recent textbooks mostly in physics, the term 'magnetic field' is used to describe Bas well as or in place of H. There are many alternative names for both (see below).

Alternative names for H
• Magnetic field intensity
• Magnetic field strength
• Magnetic field
• Magnetizing field
https://en.wikipedia.org/wiki/Magnetic_field

Here's Hyperphysics on it:

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magfield.html

Perhaps you could ask your profs to help you with this question as they will give you a better and more trusted answer from what you've been taught.