Maximum electrostatic force problem

[japam]

im studyng electromechanics and this is a problem i found

gived a fixed point A charged with Q1 charge,
gived a electrical wire of fix length L and charge Q2 distributed uniformly in it,
the wire is fixed at its edges at 2 points along a line L,
the line L and the point A are separated by a fixed distance s
to find the curve of the wire that provides the strongest attraction to the fixed point
the wire is supposed withouth weight

somebody could explain what are the math involved here? thanks

 

[zmike]

This problem is related to the physics of electric fields and can be solved using the formula for the electric field at a point due to a wire with uniform charge. The equation for the electric field E due to the wire is given by:
E = (Q2/2πεs) ln(s/L)
where ε is the permittivity of free space, s is the distance from the point A to the wire, and L is the length of the wire.

To determine the curve of the wire that provides the strongest attraction to the fixed point, you need to find the maximum value of the electric field equation. To do this, you can take the derivative of the equation with respect to s and set it equal to zero. From this, you can determine the value of s that maximizes the electric field, which will correspond to the curve of the wire that provides the strongest attraction to the fixed point.

 

[Graeme Robinson]

The problem you have described is known as a maximum electrostatic force problem. It involves finding the curve of a wire that will provide the strongest attraction to a fixed point A, given the charge distribution along the wire and the distance between the wire and the fixed point. This type of problem is commonly encountered in the field of electromechanics, as it relates to the forces and interactions between charged objects.

To solve this problem, you will need to use principles from electrostatics, such as Coulomb's law, which describes the force between two charged objects. You will also need to apply concepts of calculus, such as finding the derivative of a function, to determine the maximum force at a given point on the curve of the wire. Additionally, you may need to use techniques from vector calculus to consider the direction of the force at different points along the wire.

It is important to carefully consider the given parameters, such as the charge on the fixed point and the charge distribution along the wire, in order to accurately calculate the maximum force. You may also need to make some assumptions, such as assuming that the wire is weightless, in order to simplify the problem and make it more manageable.

Overall, this problem requires a combination of mathematical skills, as well as a deep understanding of electrostatics and its applications. It is a challenging and interesting problem that will help you develop your problem-solving abilities and deepen your understanding of electromechanics.