Electric-field strength inside a solenoid

[HeLLz aNgeL]

guys, here's my question:

A long solenoid has circular cross section of radius R. The solenoid current is increasing, and as a result so is the magnetic field in the solenoid. The field strength is given by B = bt, where b is a constant.

http://session.masteringphysics.com/problemAsset/1036090/8/RW-27-34-1.jpg

Find an expression for the electric-field strength inside the solenoid a distance r from the axis.

Express your answer in terms of the variables B, r, R and t.

could anyone help me get started... i really have no clue on this one..

thanks !

 

[christof6869]

I actually have a question related to this.

In my case, the magnetic field is coming out of the page and there is a positively charged particle initially at rest a distance "r" from the axis of the solenoid. Then, the current in the solenoid is flipped the other way instantaneously (all of the conditions are ideal here). The problem wants me to describe the trajectory of the particle. We know the mass, m, and the charge, q, of the particle as well as the current, I, and the magnetic field, B.

As for my attempt at the solution:
I think the particle doesn't initially move because of the magnetic field because the initial velocity is zero. Perhaps the instantaneous flip of current induces some sort of electric field INSIDE the solenoid. I'm not sure about the direction (into the page, out of the page, tangential to a loop of radius r) or nature of the field, but I'm fairly certain that once it starts moving, the positive particle will be redirected by the uniform magnetic field "B" to move in a left-handed helix (of radius r?) about the solenoid axis.

Am I somewhat on the right track? There is very little info about the electric field in a solenoid so any help would be greatly appreciated. Thanks.

 

[kerimek]

I would first acknowledge that this is a complex question and may require some mathematical calculations to solve. Additionally, I would suggest consulting with a physics textbook or seeking guidance from a physics professor or colleague for a more detailed explanation.

However, to get started, we can use the equation for electric field strength, E, which is given by E = -dΦ/dt, where Φ is the magnetic flux. In this case, the magnetic flux is given by Φ = BA, where A is the cross-sectional area of the solenoid.

Substituting the given equation for B into the equation for Φ, we get Φ = bAt. Taking the derivative with respect to time, we get dΦ/dt = bA. Since A = πr^2, we can rewrite this as dΦ/dt = bπr^2.

Now, we can plug this into the equation for electric field strength to get E = -dΦ/dt = -bπr^2.

However, this only gives us the electric field strength at a specific time, t. To get the expression for the electric field strength at any time, we can also include the time variable, t, in the equation. This gives us the final expression for electric field strength inside the solenoid at a distance r from the axis as:

E = -bπr^2t

I hope this helps to get you started on solving this problem. Remember to always consult reliable sources and seek guidance when dealing with complex scientific concepts.