Magnitude of external electric force on electric dipole

[ChiralSuperfields]

Homework Statement

Please see below

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!

 

[TSny]

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 $|-qE + qE|$?

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]

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!

 

[Orodruin]

Thanks for your help @TSny! The value of View attachment 318601 is zero. And the value of View attachment 318602 is 2qE, correct?

Many thanks!

Wrong. The difference is taken before the magnitude.

 

[ChiralSuperfields]

Wrong. The difference is taken before the magnitude.

Ok thank you for pointing that out @Orodruin !

 

[kuruman]

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]

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

 

[kuruman]

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?

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.

 

[ChiralSuperfields]

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!

 

[haruspex]

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 $(x^2+y^2)$.

 

[kuruman]

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]

Thank you @haruspex and @kuruman for your help, I understand now!

 

[Orodruin]

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]

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 !