7 votes
Accepted

Why does a changing magnetic flux induce an EMF in "opposite direction"?

Besides the answer "because that's how the maths works", there is a conservation of energy argument. Consider a dipole magnet, which you drop through a metal tube. As it falls, it creates a ...
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4 votes

Why does a changing magnetic flux induce an EMF in "opposite direction"?

Actually the Lenz law is connected to energy conservation (one of the most fundamental "law" of nature). So let us suppose you have a fixed conducting loop and a movable magnet. If you move ...
  • 7,270
3 votes

Can you use electrical appliances inside a Faraday's Cage?

Can you use electrical appliances inside a Faraday's Cage? Yes. I have read that if a charge was to be placed inside the cavity of a Faraday's Cage, its electric field would be canceled by the field ...
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3 votes

Magnetic force is a no work force. Why is it doing work here?

This answer adds little – except, perhaps, some linking passages – to the comments already made. The rod's velocity is shared by the free electrons in it, and therefore these experience a magnetic ...
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2 votes

What type of electric field is created by time varying magnetic field?

Yes, the electric field $\mathbf{E}$ induced by a time-varying magnetic field $\mathbf{B}$ is according to Faraday's law of induction $$\mathbf{\nabla}\times\mathbf{E}=- \frac{\partial\mathbf{B}}{\...
1 vote
Accepted

Induced emf without flux change

You assume unphysical magnetic field (magnetic field violating the condition of zero divergence, sometimes called the Gauss law of magnetism). You can see this by figuring out magnetic flux through a ...
1 vote

Doubling the length of a solenoid doubles its inductance. Two identical solenoids in series have up to four times the inductance due to M. Why?

But this case is identical to the first case where we simply doubled the length of the original inductor and doubled the number of turns to get $L_{new}=2L_0$ so we have a contradiction. How can this ...
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1 vote

Inductor connected to an AC source

To formalize all the previous answers, model the switch by a step function: $$ H(t) =\begin{cases}0 & t< 0\\1 & t \geq 0\end{cases} $$ And use it to limit the power source to positive t. ...
  • 1,625
1 vote
Accepted

Inductor connected to an AC source

Both your equations are correct as they are for different situations with the equation the general one $i=\frac{V_0}{L\omega }(1-\cos\omega t) = \frac{V_0}{L\omega } - \frac{V_0}{L\omega }\cos\omega t$...
  • 80.9k
1 vote

Inductor connected to an AC source

it is printed in my textbook that the value of $c$ equals zero, This is incorrect. It should say that $c$ is the value that makes the current equal to zero at $t=0$. $$i(t=0) =-\frac{V_0}{L\omega }\...
  • 23.9k
1 vote

Inductor connected to an AC source

The typical textbook treatment of an inductor to which $V=V_0 \sin\ \omega t$ is applied 'shows' the current to be $I=I_0 \frac 1{L\omega} \sin\ (\omega t-\frac{\pi}2)=-I_0\frac 1{L\omega} \cos \omega ...
  • 28.9k
1 vote
Accepted

What effects do inductors have on circuits?

Inductors only play a part in a circuit if the current through them is changing and then the act ny producing an emf so as to try and oppose the change. If the current through an inductor is ...
  • 80.9k
1 vote

What type of electric field is created by time varying magnetic field?

The electric field in the potential formulation takes the form: $$\vec{E} = -\nabla V - \frac{\partial\vec{A}}{\partial t}$$ In the coulomb gauge; The term $-\nabla V$ is purely divergent. ie - is ...
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1 vote

Can you use electrical appliances inside a Faraday's Cage?

However, using this logic, I find it hard to understand why scientists often conduct experiments in rooms designed as Faraday Cages with electrical equipment, in order to reduce interference from ...
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1 vote
Accepted

Am I misunderstanding the concept of magnetic flux?

$$\phi_{B}=\iint \vec{B} \cdot \vec{da}$$ If your surface is changing, as with the moving rod example, the bounds of the integral need to vary with time Assuming that the B field function exists in ...
  • 5,325
1 vote

Doubt regarding the calculation of EMF due to self-inductance and mutual inductance

As suggested by Jan, your sentence about self-induction The self-induced EMF is equal to the negative of the change in the net magnetic flux passing through the inductor is wrong. A valid sentence ...
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1 vote
Accepted

Force components on dipole falling through copper ring

Your error is assuming that $$ \int_0^{2\pi} \left[ IRB_z \hat{\rho}\right] \; d\phi = \left[\int_0^{2\pi} IRB_z\; d\phi \right]\hat{\rho}. $$ This is because at different points on the wire, the ...
1 vote
Accepted

Why is the flux linkage of one coil with respect to the other always equal if they are coaxial

No, it doesn't need to assume the fields outside the solenoid are zero. The use of long solenoids is convenient because you can compute the flux easily and do the integrals easily. But you could also ...
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