Calculating Force Between Two Dipoles With 10pC*m and 16pC*m

[vabamyyr]

there are 2 dipoles. One with electrical moment 10pC*m and other 16pC*m. The distance between 2 dipoles is 20 mm. Dipole moments are located on the same line and are pointed in the same direction. The question is what is the force between 2 dipoles.

What i have achieved so far:

i think a way is to use Coulomb`s law. We look one dipole and add the forces that exist in the one-pole system.
the interaction between two dipoles as simply the sum of four pairwise terms which are dependent on the distances between the four charges of the dipoles (pos1-pos2, neg1-neg2, pos1-neg2 and neg1-pos2). i know that p=q*l
l is distance between +q and -q in one pole. in that summing equation i don't know l1, l2, q1, q2. There is also force of field E. When i have one dipole and whatever distance r from its center then E=k*p/r^3. But how to use this knowledeg remains yet a mystery for me.

Can someone help me?

 

[ehild]

there are 2 dipoles. One with electrical moment 10pC*m and other 16pC*m. The distance between 2 dipoles is 20 mm. Dipole moments are located on the same line and are pointed in the same direction. The question is what is the force between 2 dipoles.

What i have achieved so far:

i think a way is to use Coulomb`s law. We look one dipole and add the forces that exist in the one-pole system...

You are on the right track. Derive the force on one dipole from the other in terms of the charges (q1, q2) and lengths (l1 and l2) of both dipoles and the distance R between their centers. Expand this formula in terms of l1/R and l2/R up to the non-vanishing second order terms in d1/R and d2/R. This epression will contain the product q1*l1 and q2*l2, which you can replace by p1 and p2.

ehild

 

[wais]

Your approach of using Coulomb's law is correct. The force between two dipoles can be calculated by summing the individual forces between each pair of charges in the dipoles. The formula for the force between two charges is F = (k*q1*q2)/r^2, where k is the Coulomb's constant, q1 and q2 are the charges, and r is the distance between them.

In this case, we have two dipoles with dipole moments of 10pC*m and 16pC*m, respectively. Since they are pointed in the same direction and located on the same line, we can treat them as two individual charges with a distance of 20 mm between them.

Using the formula for the force between two charges, we can calculate the force between the two dipoles as:

F = (k*(10pC*m)*(16pC*m))/(0.02m)^2 = 8.64 x 10^-6 N

This result is the net force between the two dipoles, taking into account the interaction between all four charges.

As for your question about the distance between the charges, the l1 and l2 values represent the distance between the charges in each individual dipole. In this case, both dipoles have a distance of 20 mm between their positive and negative charges, so l1 and l2 would both be 0.02 m. Similarly, q1 and q2 represent the charges in each dipole, which in this case are 10pC and 16pC, respectively.

Overall, the key concept to remember is that the force between two dipoles is the sum of the forces between each pair of charges in the dipoles. By using Coulomb's law and considering the distance and charge values for each dipole, we can calculate the net force between the two dipoles. I hope this helps clarify your understanding.