<p>It depends on what object it's acting on.  There are many objects, including stars, that have magnetic fields where <a href="https://en.wikipedia.org/wiki/Lorentz_force" rel="noreferrer">Lorentz forces</a> on charged particles like electrons and protons are stronger than the gravitational force on them. </p>

<p>Also remember that the strength of the Lorentz force depends on the speed of the particle moving through it, so a fast enough moving electron even here on Earth will receive a larger magnetic force than a force of gravity. This is how the Earth's magnetic field is able to contain charged particles in the Van Allen belts that its gravity could not contain.</p>

CC BY-SA 4.0
2019-05-30T04:55:01.367Z
Excellent! `+1` I totally forgot about the Lorentz force experienced by *charged particles* and just did [plain old static magnetic force versus gravitational force](https://astronomy.stackexchange.com/a/32101/7982).
uhoh
CC BY-SA 4.0
2019-05-30T09:35:51.963Z
Nice answer to a somehow ill posed question
Alchimista
CC BY-SA 4.0
2019-05-30T12:38:34.193Z
+1 also for pointing out the big difference. Gravity is unaffected by (discrete || <<< c) speed while Lorentz force is.
Mindwin Remember Monica
CC BY-SA 4.0
2019-05-30T12:40:27.343Z
@Alchimista That is the Pearls >>> Sand the Stack runs on. Scoop the bottom of the ocean. Questions are like sand but the scooped section may contain pearls somewhere. A question can be measured by the quality of the answers it sparked.
Mindwin Remember Monica
CC BY-SA 4.0
2019-05-30T23:08:29.007Z
@Mindwin Thank You very much. I actually put much thought in the question. How would you word it?
Muze
CC BY-SA 4.0
2019-05-31T15:03:32.667Z
@muze I don't know. The question's purpose is trifold: to solve your doubts as the OP, spark experts to post their knowledge and work as a repository of knowledge for future users. The actual wording of the question is important to understand what is being asked and to help index the search engines, but beyond that feel free to phrase it as you like. I see no problems with this one. I can understand the problem and it is elegant in its simplicity.
Mindwin Remember Monica
CC BY-SA 4.0
2019-05-31T18:19:02.770Z
@Mindwin I am glad I can draw new minds like your own and thank you and nice answer to Ken G.
Muze
CC BY-SA 4.0
2019-06-01T11:56:24.907Z
@muze thanks for the compliment, but I am not exactly new. =) P.S.: Keep doing the awesome.
Mindwin Remember Monica
CC BY-SA 4.0
2019-05-30T00:49:32.330Z
2019-05-30T04:44:18.087Z
2019-05-30T04:44:18.087Z
Ken G
<p>It isn't impossible, but the short answer is "no".</p>

<p>A gravitational field will accelerate all matter and energy equally while a magnetic field will only accelerate moving electric charges (other magnets).</p>

<p>The force due to gravity is proportional to the <em>inverse square</em> of the distance, and the force due to magnetism asymptotically approaches the <em>inverse cube</em> of the distance. At some critical distance the gravitational force will become stronger than the magnetic force.</p>

<p>Unless most of the large body was magnetic, even over the magnetic poles the magnetic field would probably be too low to levitate a typical magnet in the large body's gravitational field.</p>

CC BY-SA 4.0
2019-05-30T22:49:18.020Z
Electrons have large magnetic moments and small mass, so there might be a chance for them, and [ortho-positronium](https://en.wikipedia.org/wiki/Positronium#States)  has a magnetic moment, small mass, and is *uncharged* so there wouldn't be any Lorentz force.
uhoh
CC BY-SA 4.0
2019-06-04T19:11:21.467Z
Excellent comment.  Bottom line is that magnetic forces exceed gravitational forces only if the object is tiny, such as an electron or an atom.
PERFESSER CREEK-WATER
CC BY-SA 4.0
2019-06-05T01:04:42.980Z
Still here? just wandering?
Muze
CC BY-SA 4.0
2019-05-30T20:43:37.203Z
2019-05-30T20:43:37.203Z
anonymous
<p>Let's look at the proper magnetic force (as opposed to the <a href="https://en.wikipedia.org/wiki/Lorentz_force" rel="noreferrer">Lorentz</a> force on a <em>moving, charged object</em> described in <a href="https://astronomy.stackexchange.com/a/32097/7982">@KenG's answer</a>) on a specimen <span class="math-container">$S$</span> of magnetized material with mass <span class="math-container">$M_S$</span> as a way to try to compare. Let's arbitrarily assume it has a fixed, permanent magnetic moment <span class="math-container">$m_S$</span>. We can't use iron because it will saturate too easily. </p>

<p>Then let's look at how the forces scale differently with distance</p>

<p><span class="math-container">$$\mathbf{F_G} = -\frac{G M_S M}{r^2}\mathbf{\hat{r}} \tag{1}$$</span></p>

<p><span class="math-container">$$\mathbf{F_B} =\nabla (\mathbf{m_S} \cdot \mathbf{B}(\mathbf{r})) \tag{2}$$</span></p>

<p>If we reduce these to scalar equations at a radius <span class="math-container">$R$</span> (assume <span class="math-container">$\mathbf{m_S}$</span> and <span class="math-container">$\mathbf{B}$</span> are parallel) assume all forces are attractive, and evaluate the potentials and their gradients on the equator of the body <em>at it's physical radius</em> <span class="math-container">$R$</span>. Since the magnetic force on our dipole specimen drops off faster than the gravitational force, we have to evaluate the two at the closest physically possible distance:</p>

<p><span class="math-container">$$F_G = \frac{G M_S M}{R^2} \tag{3}$$</span></p>

<p><span class="math-container">$$F_B = \frac{3 m_S B_{r=R}}{R} \tag{4}$$</span></p>

<p>where our specimen is a distance <span class="math-container">$R$</span> from our field source, and it's moment <span class="math-container">$m_S$</span> is a magnetization of 1 Tesla times the volume of a 1 kg rare earth magnet, about 0.000125 cubic meters.</p>

<p>All MKS units, all rough, ballpark numbers with emphasis on strongest magnetic fields</p>

<pre><code>Body             R (m)      M (kg)    B(r=R) (T)    F_G  (N)    F_B (N)    F_B/F_G
Earth            6.4E+06    6.0E+24   5.0E-05       9.8E+00     2.9E-15    3.0E-16
Jupiter          7.1E+07    1.9E+27   4.2E-04       2.5E+01     2.2E-15    8.8E-17
Neutron Star     1.0E+04    4.0E+30   5.0E+10       2.7E+12     1.9E+03    7.0E-10
Magnetar         1.0E+04    4.0E+30   2.0E+11       2.7E+12     7.6E+03    2.8E-09
</code></pre>

<p>So even for a <a href="https://en.wikipedia.org/wiki/Magnetar" rel="noreferrer">Magnetar</a> (see also <a href="https://arxiv.org/abs/1703.00068" rel="noreferrer">1</a>, <a href="http://www.physics.mcgill.ca/~pulsar/magnetar/main.html" rel="noreferrer">2</a>) a kind of neutron star with a very strong magnetic field), the magnetic force on our 1kg specimen of permanent magnet is only 3 parts per billion as strong as the gravitational force.</p>

<p>You might see a much more favorable ratio if you compared two subatomic particles at short ranges (e.g. 1E-15 meters) but for astronomical objects, gravity seems to win smartly.</p>

CC BY-SA 4.0
2019-05-31T07:45:37.027Z
I don't think your expression for magnetic force is correct. For a magnetic material it should depend on $B^2$. And if you are putting in $G$ and using SI units, then where is the $\mu_0/4\pi$?
ProfRob
CC BY-SA 4.0
2019-05-31T07:48:59.337Z
@RobJeffries the word "magnetic" is an artifact from a previous version and I'll change it to "magnetized". The next sentence states that it's a permanent magnet with magnetic moment $\mathbf{m_S}$ (1 kg, density of about 8000 kg/m^2, 1 Tesla magnetization) and later I mention that we can assume $\mathbf{m_S}$ and $B$ to be parallel (or antiparallel) It's of course preposterous to put a magnet near the surface of a neutron star (unless it's in a [General Products hull](https://scifi.stackexchange.com/q/128375/51174)). I just want to show that gravity wins by a landslide.
uhoh
CC BY-SA 4.0
2019-06-01T22:52:12.533Z
Comments are not for extended discussion; this conversation has been [moved to chat](https://chat.stackexchange.com/rooms/94397/discussion-on-answer-by-uhoh-can-a-magnetic-field-of-an-object-be-stronger-than).
called2voyage
CC BY-SA 4.0
2019-05-30T04:40:37.280Z
2019-05-31T07:51:21.737Z
2019-05-31T07:51:21.737Z
uhoh
<p>Can a planet, star or otherwise have a magnetic field that is stronger or have more range than its gravity?</p>

CC BY-SA 4.0
2019-05-30T04:40:53.970Z
interesting question!
uhoh
CC BY-SA 4.0
2019-05-30T16:44:12.213Z
Magnetar?  "The magnetic field of a magnetar would be lethal even at a distance of 1000 km due to the strong magnetic field distorting the electron clouds of the subject's constituent atoms, rendering the chemistry of life impossible": https://en.wikipedia.org/wiki/Magnetar
jamesqf
CC BY-SA 4.0
2019-05-31T07:37:00.597Z
Magnetic field and force have different units/dimensions and cannot be compared directly.
ProfRob
CC BY-SA 4.0
2019-05-31T07:57:10.083Z
At what point does a black hole with charge and angular momentum become (super-) extremal?
JollyJoker
CC BY-SA 4.0
2019-05-31T11:37:57.680Z
@Jamesqf Proton precession ...?
Russell McMahon
CC BY-SA 4.0
2019-05-31T19:11:34.840Z
@uhoh remember that question of using a diamagnetic sail off a Sun spot? This is related to that, but off topic here.
Muze
CC BY-SA 4.0
2019-05-31T23:03:15.363Z
While both electromagnetism and gravitational fields have infinite range, magnetic fields generally fall off as 1 / r^3 rather than 1 / r^2 for gravity.
J. O'Brien Antognini
CC BY-SA 4.0
2019-06-01T06:57:00.360Z
It would seem to me that for a pair of ordinary permanent magnets, their gravitational interaction is negligible compared to their magnetic interaction. So if "or otherwise" is to allow for small objects at small distances, the answer would appear to be positive.
Marc van Leeuwen
CC BY-SA 4.0
2019-06-01T09:32:20.100Z
@MarcvanLeeuwen Heck, is there anything stopping someone from just scaling up a bar magnet into a giant planet-sized bar magnet?
nick012000
<gravity><fundamental-astronomy><magnetic-field><stellar-astrophysics><stellar-dynamics>
Can a magnetic field of an object be stronger than its gravity?
Muze
# Can a magnetic field of an object be stronger than its gravity?

(Asked by: username_0 on 2019-05-30)

Can a planet, star or otherwise have a magnetic field that is stronger or have more range than its gravity?

**Tags:** gravity, fundamental-astronomy, magnetic-field, stellar-astrophysics, stellar-dynamics

> **Comments:**
> **username_1**: interesting question!  
> **username_2**: Magnetar?  "The magnetic field of a magnetar would be lethal even at a distance of 1000 km due to the strong magnetic field distorting the electron clouds of the subject's constituent atoms, rendering the chemistry of life impossible": https://en.wikipedia.org/wiki/Magnetar  
> **username_3**: Magnetic field and force have different units/dimensions and cannot be compared directly.  
> **username_4**: At what point does a black hole with charge and angular momentum become (super-) extremal?  
> **username_5**: @Jamesqf Proton precession ...?  
> **username_0**: @username_1 remember that question of using a diamagnetic sail off a Sun spot? This is related to that, but off topic here.  
> **username_6**: While both electromagnetism and gravitational fields have infinite range, magnetic fields generally fall off as 1 / r^3 rather than 1 / r^2 for gravity.  
> **username_7**: It would seem to me that for a pair of ordinary permanent magnets, their gravitational interaction is negligible compared to their magnetic interaction. So if "or otherwise" is to allow for small objects at small distances, the answer would appear to be positive.  
> **username_8**: @MarcvanLeeuwen Heck, is there anything stopping someone from just scaling up a bar magnet into a giant planet-sized bar magnet?  

---

## 3 answers

### Answer by username_1 on 2019-05-30. Score: 17 | Accepted answer

Let's look at the proper magnetic force (as opposed to the Lorentz force on a moving, charged object described in @KenG's answer) on a specimen $S$ of magnetized material with mass $M_S$ as a way to try to compare. Let's arbitrarily assume it has a fixed, permanent magnetic moment $m_S$. We can't use iron because it will saturate too easily. 
Then let's look at how the forces scale differently with distance
$$\mathbf{F_G} = -\frac{G M_S M}{r^2}\mathbf{\hat{r}} \tag{1}$$
$$\mathbf{F_B} =\nabla (\mathbf{m_S} \cdot \mathbf{B}(\mathbf{r})) \tag{2}$$
If we reduce these to scalar equations at a radius $R$ (assume $\mathbf{m_S}$ and $\mathbf{B}$ are parallel) assume all forces are attractive, and evaluate the potentials and their gradients on the equator of the body at it's physical radius $R$. Since the magnetic force on our dipole specimen drops off faster than the gravitational force, we have to evaluate the two at the closest physically possible distance:
$$F_G = \frac{G M_S M}{R^2} \tag{3}$$
$$F_B = \frac{3 m_S B_{r=R}}{R} \tag{4}$$
where our specimen is a distance $R$ from our field source, and it's moment $m_S$ is a magnetization of 1 Tesla times the volume of a 1 kg rare earth magnet, about 0.000125 cubic meters.
All MKS units, all rough, ballpark numbers with emphasis on strongest magnetic fields
Body             R (m)      M (kg)    B(r=R) (T)    F_G  (N)    F_B (N)    F_B/F_G
Earth            6.4E+06    6.0E+24   5.0E-05       9.8E+00     2.9E-15    3.0E-16
Jupiter          7.1E+07    1.9E+27   4.2E-04       2.5E+01     2.2E-15    8.8E-17
Neutron Star     1.0E+04    4.0E+30   5.0E+10       2.7E+12     1.9E+03    7.0E-10
Magnetar         1.0E+04    4.0E+30   2.0E+11       2.7E+12     7.6E+03    2.8E-09

So even for a Magnetar (see also 1, 2) a kind of neutron star with a very strong magnetic field), the magnetic force on our 1kg specimen of permanent magnet is only 3 parts per billion as strong as the gravitational force.
You might see a much more favorable ratio if you compared two subatomic particles at short ranges (e.g. 1E-15 meters) but for astronomical objects, gravity seems to win smartly.

> **Comments:**
> **username_3**: I don't think your expression for magnetic force is correct. For a magnetic material it should depend on $B^2$. And if you are putting in $G$ and using SI units, then where is the $\mu_0/4\pi$?  
> **username_1**: @RobJeffries the word "magnetic" is an artifact from a previous version and I'll change it to "magnetized". The next sentence states that it's a permanent magnet with magnetic moment $\mathbf{m_S}$ (1 kg, density of about 8000 kg/m^2, 1 Tesla magnetization) and later I mention that we can assume $\mathbf{m_S}$ and $B$ to be parallel (or antiparallel) It's of course preposterous to put a magnet near the surface of a neutron star (unless it's in a [General Products hull](https://scifi.stackexchange.com/q/128375/51174)). I just want to show that gravity wins by a landslide.  
> **username_14**: Comments are not for extended discussion; this conversation has been [moved to chat](https://chat.stackexchange.com/rooms/94397/discussion-on-answer-by-username_1-can-a-magnetic-field-of-an-object-be-stronger-than).  

---

### Answer by username_9 on 2019-05-30. Score: 37

It depends on what object it's acting on. There are many objects, including stars, that have magnetic fields where [Lorentz forces](https://en.wikipedia.org/wiki/Lorentz_force) on charged particles like electrons and protons are stronger than the gravitational force on them.

Also remember that the strength of the Lorentz force depends on the speed of the particle moving through it, so a fast enough moving electron even here on Earth will receive a larger magnetic force than a force of gravity. This is how the Earth's magnetic field is able to contain charged particles in the Van Allen belts that its gravity could not contain.

> **Comments:**
> **username_1**: Excellent! `+1` I totally forgot about the Lorentz force experienced by *charged particles* and just did [plain old static magnetic force versus gravitational force](https://astronomy.stackexchange.com/a/32101/7982).  
> **username_10**: Nice answer to a somehow ill posed question  
> **username_11**: +1 also for pointing out the big difference. Gravity is unaffected by (discrete || <<< c) speed while Lorentz force is.  
> **username_11**: @username_10 That is the Pearls >>> Sand the Stack runs on. Scoop the bottom of the ocean. Questions are like sand but the scooped section may contain pearls somewhere. A question can be measured by the quality of the answers it sparked.  
> **username_0**: @Mindwin Thank You very much. I actually put much thought in the question. How would you word it?  
> **username_11**: @muze I don't know. The question's purpose is trifold: to solve your doubts as the OP, spark experts to post their knowledge and work as a repository of knowledge for future users. The actual wording of the question is important to understand what is being asked and to help index the search engines, but beyond that feel free to phrase it as you like. I see no problems with this one. I can understand the problem and it is elegant in its simplicity.  
> **username_0**: @Mindwin I am glad I can draw new minds like your own and thank you and nice answer to username_9.  
> **username_11**: @muze thanks for the compliment, but I am not exactly new. =) P.S.: Keep doing the awesome.  

---

### Answer by username_12 on 2019-05-30. Score: 9

It isn't impossible, but the short answer is "no".

A gravitational field will accelerate all matter and energy equally while a magnetic field will only accelerate moving electric charges (other magnets).

The force due to gravity is proportional to the *inverse square* of the distance, and the force due to magnetism asymptotically approaches the *inverse cube* of the distance. At some critical distance the gravitational force will become stronger than the magnetic force.

Unless most of the large body was magnetic, even over the magnetic poles the magnetic field would probably be too low to levitate a typical magnet in the large body's gravitational field.

> **Comments:**
> **username_1**: Electrons have large magnetic moments and small mass, so there might be a chance for them, and [ortho-positronium](https://en.wikipedia.org/wiki/Positronium#States)  has a magnetic moment, small mass, and is *uncharged* so there wouldn't be any Lorentz force.  
> **username_13**: Excellent comment.  Bottom line is that magnetic forces exceed gravitational forces only if the object is tiny, such as an electron or an atom.  
> **username_0**: Still here? just wandering?  

---

