Magnitude of external electric force on electric dipole

• ChiralSuperfields
In summary: You're right, I misunderstood the bars. They meant "take the absolute value of what is between the bars", which is zero. Thanks for clearing that up for me!
ChiralSuperfields
Homework Statement
Relevant Equations
Torque = electric dipole moment x electric field strength
For this part(b) of this problem, how is the magnitude of the total electric force zero?

I thought it would be:

If they asked for the total electric force, then I would have said zero because the two electric force vectors cancel.

Many thanks!

Attachments

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Callumnc1 said:
For this part(b) of this problem, how is the magnitude of the total electric force zero?

I thought it would be:
View attachment 318599
What is the value of ##-qE + qE##? What is the value of ##|-qE + qE|##?

Callumnc1 said:
If they asked for the total electric force, then I would have said zero because the two electric force vectors cancel.
Yes, the total electric force vector is the zero vector. So, the magnitude of the total electric force is the magnitude of the zero vector.

If they had asked for the sum of the magnitudes of the two forces, then you would get ##2qE##. But this doesn't have much physical significance. The sum of the magnitudes of two vectors is generally not the same as the magnitude of the sum of the two vectors.

ChiralSuperfields and Orodruin
TSny said:
What is the value of ##-qE + qE##? What is the value of ##|-qE + qE|##?Yes, the total electric force vector is the zero vector. So, the magnitude of the total electric force is the magnitude of the zero vector.

If they had asked for the sum of the magnitudes of the two forces, then you would get ##2qE##. But this doesn't have much physical significance. The sum of the magnitudes of two vectors is generally not the same as the magnitude of the sum of the two vectors.
Thanks for your help @TSny! The value of
is zero. And the value of
is 2qE, correct?

Many thanks!

ChiralSuperfields
Orodruin said:
Wrong. The difference is taken before the magnitude.
Ok thank you for pointing that out @Orodruin !

You could also have sorted this out if you kept in mind that force is a vector which has magnitude and direction. Both are needed to specify a vector. In this case, if the force on the dipole were ##2qE##, what would its direction be and why?

ChiralSuperfields
kuruman said:
You could also have sorted this out if you kept in mind that force is a vector which has magnitude and direction. Both are needed to specify a vector. In this case, if the force on the dipole were ##2qE##, what would its direction be and why?
Thanks for your reply @kuruman ! Is it not impossible for the force on the dipole to be 2qE since the charges are equal and opposite?

Many thanks,
Callum

It is impossible for the force on the dipole to be 2qE. I was referring to this statement in post #1 where you seem to think that it is 2qE. Did I miss your point? What did you think would be 2qE?

Callumnc1 said:
I thought it would be:
View attachment 318599
If they asked for the total electric force, then I would have said zero because the two electric force vectors cancel.

Thanks for your reply @kuruman! I though the magnitude of the force was 2qE because I though
. But apparently absolute values bars don't work like that.

I guess 2qE would be the magnitude of the external electric force on each side of the dipole added together, correct?

Many thanks!

Callumnc1 said:
apparently absolute values bars don't work like that.
They could not work like that. The bars mean "take the absolute value of what is between the bars". What is between the bars is -qE+qE, which is zero.
Likewise ##(x+y)^2## is not the same as ##(x^2+y^2)##.

ChiralSuperfields
Callumnc1 said:
apparently absolute values bars don't work like that.
The bars are like parentheses except, after you calculate what's between them, you strip the negative sign if it's there.

Example
##|5-2|=|3|=3##

##|2-5|=|-3|=3.##

ChiralSuperfields
If the net charge is zero, the net force (and hence its magnitude) can only be non-zero if the electric field is not constant. You can however have a net force on a dipole if the field is different in different points.

ChiralSuperfields
Orodruin said:
If the net charge is zero, the net force (and hence its magnitude) can only be non-zero if the electric field is not constant. You can however have a net force on a dipole if the field is different in different points.
Thank you @Orodruin !

1. What is an electric dipole?

An electric dipole is a pair of equal and opposite charges separated by a small distance. This separation creates a dipole moment, which is a measure of the strength and direction of the dipole.

2. How is the magnitude of external electric force on an electric dipole calculated?

The magnitude of the external electric force on an electric dipole can be calculated using the formula F = pE sinθ, where p is the dipole moment, E is the electric field strength, and θ is the angle between the dipole moment and the electric field.

3. What factors affect the magnitude of external electric force on an electric dipole?

The magnitude of the external electric force on an electric dipole is affected by the strength of the electric field, the distance between the charges, and the angle between the dipole moment and the electric field.

4. How does the direction of the electric field affect the magnitude of external electric force on an electric dipole?

The direction of the electric field is an important factor in calculating the magnitude of external electric force on an electric dipole. If the electric field is parallel to the dipole moment, the force will be zero. If the electric field is perpendicular to the dipole moment, the force will be at its maximum value.

5. Can the magnitude of external electric force on an electric dipole be negative?

Yes, the magnitude of external electric force on an electric dipole can be negative. This occurs when the electric field and the dipole moment are in opposite directions, resulting in a negative value for the force.

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