How Does the Speed of a Van Affect the Lorentz Force in a Magnetic Field?

[elecstudent1]

Homework Statement

Problem is http://imgur.com/bQIFJ

Homework Equations

I presume F=BIl and E=Blu.

The Attempt at a Solution

Not very well. I don't really understand how to start the question so if I could get some nudges in the right direction that'd be great. I'm not sure how the speed of the van comes into play here. I gather that I'll have to work out V once for the 38uT field density and then again for the 42uT and get the difference.

 

[kushan]

You can find it using E= Bul

 

[Simon Bridge]

This is an induction problem - the current induced is proportional to the change in magnetic induction (B) inside the coil.
http://physics.bu.edu/~duffy/PY106/InducedEMF.html

 

[NoPoke]

I don't think the question has enough information. A loop of wire will not produce any output voltage unless the field is varying. To calculate the output you need the rate at which the field is varying. Vehicle speed plus the two field strengths is not enough to establish the rate of change of the field.

The equation you need is V = - N d(phi)/dt

Do you have a picture/drawing of what this "detector" looks like?

 

[Nickie]

First, it is important to understand the concept of electromagnetism and how it relates to the speed of an object in a field. Electromagnetism is the study of the relationship between electricity and magnetism. When a charged particle moves through a magnetic field, it experiences a force known as the Lorentz force, which is given by the equation F = qv x B, where q is the charge of the particle, v is its velocity, and B is the magnetic field.

In this problem, we are given the magnetic field strength, B, as well as the current, I, and the length of the wire, l. This allows us to calculate the force experienced by the van, using the equation F = BI l. This force will act in the direction perpendicular to both the magnetic field and the direction of the current.

Next, we need to consider the velocity of the van. The problem states that the van is moving at a constant speed, which means that the net force acting on it must be zero. This means that the Lorentz force must be balanced by some other force, such as friction or the force of the engine. However, since we are only given information about the magnetic field, we can assume that the other forces are negligible.

Therefore, we can set the Lorentz force equal to zero and solve for the velocity, v, using the equation F = qv x B. We can then repeat this calculation for the different values of the magnetic field, B, and compare the velocities to determine the difference.

It is also worth noting that the electric field, E, is related to the magnetic field, B, through the equation E = Blu, where u is the velocity of the charged particle. This equation can be used to calculate the electric field, which could be useful in solving this problem.

In summary, to solve this problem, we need to calculate the Lorentz force acting on the van using the given information, set it equal to zero to find the velocity, and then repeat this calculation for the different values of the magnetic field to determine the difference in velocity. We can also use the equation for the electric field to aid in our calculation.