# Homework Help: Magnetic Field and Electric field outside a long solenoid

1. Feb 5, 2006

### darkar

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?

2. Feb 7, 2006

### anaemic1

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: Feb 7, 2006
3. Feb 7, 2006

### Staff: Mentor

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. Feb 11, 2006

### darkar

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, thats the correct answers! but i am still not sure why it is not zero. isnt that when theres no magnetic field, theres no electric field as well?

5. Feb 11, 2006

### Physics Monkey

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. Feb 12, 2006

### darkar

Yea, thats amaze me. Why can there be magnetic flux but no magnetic field. So lif theres magnetic field, the magnetic flux is constant?

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