Needle suspended from string - dipole moment?

[ibaraku]

Homework Statement

A needle suspended from a string hangs horizontally. The electrical field at the needle's location is horizontal with magnitude 3.7 x 10^3 N/C
and it's at an angle of 30 degrees with the needle. There is no net electrical force acting on the needle, but the string exerts a torque of 3.7 x 10^-4 Nm to hold the needle in equilibrium. What is the needle dipole moment?

Homework Equations

t = torque
p = dipole moment
E = electric field

t = p x E

The Attempt at a Solution

The way I am trying to solve this seems very easy and I thought I better check before turning this in.

we want the dipole moment which is p, therefore

p = t / E -->> p = 3.7 x 10^-4 / 3.7 x 10^3

but then I'm thinking, the angle given in the problem statement come in play somewhere right?
Am I in the right track?

 

[anathema]

Hello,

Yes, you are on the right track. However, there is one small error in your calculation. The torque and electric field are both vector quantities, meaning they have both magnitude and direction. In this case, the torque and electric field are perpendicular to each other, so you cannot simply divide them. Instead, you need to use the vector cross product formula, which is t = p x E. This means that p = t / E sinθ, where θ is the angle between the torque and electric field vectors. In this case, θ = 90 degrees, so sinθ = 1. Therefore, the correct equation would be p = t / E. Plugging in the values given in the problem, we get:

p = (3.7 x 10^-4 Nm) / (3.7 x 10^3 N/C)

= 1.0 x 10^-7 Cm

So the dipole moment of the needle is 1.0 x 10^-7 Cm.

I hope this helps! Keep up the good work in your studies.

 

[baba89]

I would say that you are on the right track but may need to consider a few more factors before arriving at a complete answer. The equation you have used, p = t / E, is correct in principle as the torque is equal to the cross product of the dipole moment and the electric field. However, in this case, we are dealing with a needle that is suspended from a string, which adds another element to the problem.

Firstly, we need to consider the definition of a dipole moment. It is the measure of the separation of positive and negative charges in a system, multiplied by the magnitude of the charge. In this case, the needle is acting as a dipole with its positive and negative charges separated by a certain distance. Therefore, we need to consider the length of the needle and the distance between the charges when calculating the dipole moment.

Secondly, the angle given in the problem statement does play a role in the solution. This is because the torque on the needle is dependent on the angle between the dipole moment and the electric field. We can use the equation t = p x E x sinθ to take into account this angle and arrive at a more accurate value for the dipole moment.

Lastly, the fact that the needle is suspended from a string adds another element to the problem. The string is exerting a force on the needle to keep it in equilibrium, and this force needs to be considered when calculating the dipole moment. We can use the equation p = qd, where q is the charge and d is the distance between the charges, to take into account this force and arrive at a more accurate value for the dipole moment.

In conclusion, you are on the right track with using the equation p = t / E to calculate the dipole moment. However, to arrive at a more accurate and complete answer, you need to consider the length of the needle, the angle between the dipole moment and the electric field, and the force exerted by the string when calculating the dipole moment.