Why is the direction of electric dipole moments from negative to positive and that of a magnets is south from south to north?

Answer 1

let me try to explain it this way. Suppose I have an electric dipole that is placed in an external electric field E(vector).

Now, scientists try to calculate the energy stored in the dipole due to its position and configuration in the external field.

When you learn about angular motion, you probably know this equation that describe the potential rotational energy : delta U = U(final) - U(initial) = (integral from θ(initial) to θ(final) of the torque)

= ∫τ dθ

Let's just skip the calculation to determine the energy. But what we really need now is how to find the torque in order to estimate U.

From the figure above, you might see that we assume the field points from the left to the right, there fore it will exert a force on the two charges. For the positive charge, the force is to the right and for the negative charge, the force is to the left, but the charges attract each other.Thus they cause the electric dipole to rotate around an axis that is perpendicular to the page and pass through the centre of the line connects the charges.

The torque vector is the cross product of the displacement vector (r) and the force vector (F)

then τ = r X F = F*r*sin(θ) = F*(a)*sin(θ) (since we let a=r is half the distance from the negative charge to the positive charge and it's exactly the distance from the centre to each point charge)

And the total torque is : (total)τ = τ 1(positive) + τ 2(negative) = 2F*a*sin(θ)

But the electric force F = qE, we substitute it into the equation to get:

(total)τ = 2qEasin(θ), rearrange it, we have : (total)τ = (2qa)E(sin(θ))

Since it's easy to calculate E and θ, we let E and sin(θ) out and group two quantity a,q and the coefficient 2 as one quantity called the electric dipole moment p

So now, p = 2aq

That's how we got the magnitude of the electric dipole moment. But there's a problem since we realize that the torque (total)τ and E are all vector quantities. So that means the electric dipole moment p must also be a vector quantity so that we can perform the cross product calculation.

(total)τ(vector)= p(vector) X E(vector)

Here we have two choices, one is p points from the negative to the positive and the other is the opposite.

Let me remind you that since the electric field points from left to right, the e.dipole will definitely rotate clockwise

The toque is the vector that lies along the axis of rotation and since we have an international convention that if it rotates clockwise, the angular velocity is negative and if it rotates counter-clockwise then the angular velocity is positive

if I use the right hand rule to find the direction and sign of the angular velocity , i find that the angular velocity vector points into the page and because τ= I*(angular velocity), the torque must points in the same direction, which is into the page.

It's very clear now that τ(vector) = p(vector) x E(vector). We find the magnitude by performing this calculation: τ = pEsin(theta) and determine the direction using the right hand rule .

As we discuss earlier, τ(vector) points into the page and E is to the right, thus the only solution for the direction of the electric dipole moment vector is from the negative charge to the positive charge(not the opposite one)!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

This works well with different configurations, too.

And with that, we have a complete definition of the electric dipole moment vector that would fit and be consistent with so many previous physics laws and equations.

Good luck with this!!!