# In the Bohr model of the atom, does the centripetal force balance out the electrostatic force? [closed]

Is this picture correct?

It's the Bohr Model for electron moving around the nucleus.

In my opinion, the centripetal force should be directed towards the center, and the electrostatic force should be directed outward.

And i found a counterexample :

Plus, in all my classcial mechanics classes, the centripetal force was inward.

So can someone check this picture and tell me if it's wrong or right.

And if it's right, can you elaborate on why it is?

• Yes the centripetal force should be pointing inwards. However the electrostatic force should also be pointing inwards because the proton and electron are of opposite charge polarity. Oct 4, 2021 at 9:52
• Yes, correct him or her. He's made a "rookie error" with the words "Force due to Centripetal Acceleration". The force is not due to centripetal acceleration, it is due to the electrostatic attraction. It's important that new students understand this, as it's the cause of future confusion. Gently remind him. I'm sure he or she knows this; it's a slip-up. Oct 4, 2021 at 11:07
• It's common for novices to miss the concept that the centripetal force is not in itself a force. Centripetal force is a descriptive phrase that represents the sum of whatever real forces add to provide a constant center-oriented net force. For example, the centripetal force keeping the chairs of a Ferris wheel in uniform circular motion is a sum of the mechanical forces due to the metal structure, and gravity. Oct 4, 2021 at 11:07
• okay thanks, i'll see what can i do, huge thanks! Oct 4, 2021 at 11:18
• In this case, the centripital force pretty much is the electrostatic force. I don't believe the nuclear forces will have much effect at that distance. Oct 4, 2021 at 18:57

Yes, the arrow representing a centripetal force should point inwards.

The electrostatic force is the centripetal force here. There is only one force (the electrostatic force), the centripetal force is not something different but a way of describing what the actual force does (i.e. that it forces the object onto an orbit).

If one only wants to show real forces, then there is only one arrow showing the electrostatic force (like in the second picture), but if you want to represent both aspects, then the arrow representing the centripetal force should be exactly the same (equal in size and direction).

The first picture implies (wrongly) that there is a balance between two (equal but opposite) forces. If this was true, then the electron would not move in an orbit but in a straight line. An object on an orbit is continually accelerated towards the centre, otherwise it wouldn't follow a curved path.

• It's not that the electric force is equal to centripetal force. The electric force IS the centripetal force. There is only one force not two.
– nasu
Oct 4, 2021 at 10:51
• @nasu that's exactly what I wrote, no? Oct 4, 2021 at 10:58
• @ElieMakdissi You could show your professor the answers here and see what he thinks. But of course it depends on his personality and your situation (I had some professors who I would not want to correct as they get angry...), so you have to decide if this is good. Oct 4, 2021 at 11:01
• @Stepen Matthiesen There is a common misconception between students in intro physics that the centripetal force is some extra force that appears besides the forces due to interactions. Your formultion may propagate ths confusion as it may be interpreted that there are two forces. You say: "the centripetal force should point inwards and the electrostatic force should also point inwards". This leave room for thinking taht there are two forces which just happens to point in the same direction.
– nasu
Oct 4, 2021 at 11:27
• @Elie Makdissi: Maybe it goes without saying, but try to correct your professor privately and not in front of his class. Oct 4, 2021 at 18:39

His diagram is not wrong, it is what you will use in a noninertial frame moving with the electron. In this frame you introduce a "fictional" centrifugal force (pointing radially outwards) and Newton's second law results in an equilibrium of forces. The acceleration in this non-inertial frame is zero so the net force should be zero. He did not say that the vector pointing out is a centripetal force just that it is due to centripetal acceleration. When you switch your analysis to a noninertial frame you introduce a fictional force $$f=-m\vec{a}$$ where $$\vec{a}$$ is the acceleration of the non-inertial sstem relative to an inertial system. In this case $$\vec{a}$$ is the centripetal acceleration. So, the figure by itself is not wrong as long it is used in the right context. I don't know what/how he actually explained in class. The second image you show represent the analysis in an inertial reference frame (fixed relative to the center of the circle). In this frame there is only one force, the interaction force (electrostatic). Both figures are OK but they represent the analysis in two different frames.

• Oh okay that's a good answer, i didn't really think about non inertial frames because the professor didn't even mention it, he just said that "centripetal force" vector is outward and with the electrostatic force adds up to zero(equilibrium) Oct 4, 2021 at 13:24

The centripetal force is the electrostatic force. So it is natural that both of them have the same direction i.e radially inwards. The charges have opposite signs and hence the force is attractive in nature.

• ah okay thanks :) Oct 4, 2021 at 10:45

There is no "outward" force

The inwards electrostatic force combined with the velocity creates the circular motion (essentially an orbit).

• thanks for the answer Oct 4, 2021 at 12:21
• but how did you edit the photo 8) Oct 4, 2021 at 12:21
• @ElieMakdissi I used greenshot to copy the picture and open it in their editor from the clipboard. The editor can add lines, arrows, draw rectangles/circles, etc. A white rectangle does wonders to remove things from the picture. Oct 4, 2021 at 12:48
• wow thanks man i'll def try it Oct 4, 2021 at 13:18

Even in a non inertial frame the force outward is called centrifugal force and not centripetal.

• The label on the diagram says it's a force that arises due to centripetal acceleration. If you want to make excuses for the diagram (and find a way for it to be technically not wrong, just misleading / confusing), you can say that the centrifugal force in the orbiting reference frame arises due to the centripetal acceleration of the reference frame. But that feels like a stretch. Oct 4, 2021 at 21:06