Magnetic Field and Electric field outside a long solenoid

In summary: It's because in this case the magnetic field is zero outside the solenoid because there are two sources of magnetic flux. The first is the field due to the currents in the solenoid, and the second is the field due to the magnetic field due to the currents in the neighboring loops. Since these fields are cancelling out, the magnetic field outside the solenoid is zero.
  • #1
darkar
187
0
Hello,

The question goes like this:

A long solenoid has n turns per unit length and carries a current given by I=I₀sinωt. The solenoid has a circular cross section of radius R. Find the induced electric field at a radios r from the axis of the solenoid for (a) r<R (b) r>R

Well, i got the first part as E=μR²N²ωI₀cos(ωt)/(2Rl). Does this looks like it?

For the second bit, i found it as zero. But i am not really sure. And if it is zero, What should i say?
 
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  • #2
Hello there,

You'll have to excuse me because I'm not using the greek symbols.

(a) r<R,

int(E.dl)=-d(B.Area)/dt (definition of induced emf) take loop around

E.2*pi*r = -pi*(r^2)*mu*n*I*omega*cos(omega*t)

E= -(mu*n*I*omega*r*cos(omega*t))/2

is the induced field inside solenoid. Your answer is close but use r instead of R (since we are inside).

(b) r>R, outside

You are confusing with the case when magnetic field is zero outside long solenoid due to cancellations between field due to currents in successive & opposite loops.

In this case, (r>R...remember loop is longer)

E*2*pi*r = -pi*(R^2)*mu*n*I*omega*cos(omega*t)

(remember flux is over an area defined by pi*(R^2))

E = -(mu*n*I*omega*(R^2)*cos(omega*t))/ (2*r)

is the induced electric field outside.Hope that helps,
Rama
 
Last edited:
  • #3
Are you sure they are asking about Electric fields? That doesn't make much sense. More often, you will be asked to solve for the magnetic field as a function of radius for the solenoid...
 
  • #4
Yea, i m asked to find electric field. And i just found out this is one of the question found from the textbook. And yes, that's the correct answers! but i am still not sure why it is not zero. isn't that when there's no magnetic field, there's no electric field as well?
 
  • #5
darkar,

To understand why there is an electric field outside the solenoid, just think about Faraday's Law. If you draw a loop around the solenoid, the magnetic flux through the loop is changing as a function of time, right? Even though there is no magnetic field outside the solenoid there is still a changing magnetic flux (from the field inside the solenoid). What does this tell you about the electric field?
 
  • #6
Yea, that's amaze me. Why can there be magnetic flux but no magnetic field. So lif there's magnetic field, the magnetic flux is constant?
 

1. What is a solenoid and how does it create a magnetic field?

A solenoid is a cylindrical coil of wire that carries an electric current. When an electric current passes through a wire, it creates a magnetic field around the wire. In a solenoid, the magnetic field lines are concentrated inside the coil, creating a strong magnetic field.

2. How does the magnetic field outside a long solenoid compare to the magnetic field inside?

The magnetic field outside a long solenoid is much weaker than the magnetic field inside. This is because the magnetic field lines are concentrated inside the coil, creating a more intense field. Outside the solenoid, the field lines spread out and the magnetic field becomes weaker.

3. Is the magnetic field uniform outside a long solenoid?

No, the magnetic field outside a long solenoid is not uniform. The magnetic field lines are closer together near the ends of the solenoid and farther apart near the middle. This is because the magnetic field is stronger near the ends of the solenoid where the field lines are more concentrated.

4. How is the electric field related to the magnetic field outside a long solenoid?

The electric field outside a long solenoid is directly proportional to the rate of change of the magnetic field with respect to time. This means that if the magnetic field is changing, an electric field will be induced outside the solenoid. This phenomenon is known as electromagnetic induction.

5. Can the direction of the magnetic field outside a long solenoid be changed?

Yes, the direction of the magnetic field outside a long solenoid can be changed by changing the direction of the electric current passing through the coil. Reversing the direction of the current will also reverse the direction of the magnetic field. This is known as the right-hand rule, where the thumb points in the direction of the current and the fingers curl in the direction of the magnetic field.

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