# current induced in magnetic field

"If a wire loop is completely in magnetic field no current is induced as voltage induced is balanced by an equal and opposite voltage. "

My guess for this statement is that the loop wire must be stationary and that voltage is zero if its equal on both sides of the wire my question is if current will stil be induced if the wire loop is moving but is still completely in the magnetic field. (I know how as it enters and leaves induced current moves either clockwise or anti so what wil happen if its moving but not entering or leaving)

• If it moving in a uniform magnetic field, no current will flow as the magnetic flux through the wire loop is constant and therefore, the net induced EMF is zero.($\int_{loop} \vec E \cdot \vec {dl}=-d\phi /dt$) But if it moves in a non-uniform field, there may be a current in the loop. – Satwik Pasani Sep 24 '13 at 12:12
• @SatwikPasani If it moves in a non-uniform field, there can be an EMF, however the EMF will be equal to $\oint_{loop}\vec{f}_m\cdot d\vec{\ell}$ where $\vec{f}_s$ is the magnetic force per unit charge. The EMF of $\oint_{loop}\vec{E}\cdot d\vec{\ell}$ is actually equal to the negative of the instantaneous flux of the change of the $\vec{B}$ field, $-\iint \frac{\partial \vec{B}}{\partial t}\cdot d\vec{a}$. – Timaeus Feb 12 '15 at 2:33

## 2 Answers

Electrical generators work by moving loops of conductive material through magnetic fields. These conductors never leave the fields.

Saying that a wire loop is "completely" inside a magnetic field is rather inane. The condidtion that has to be met is that either the field is uniform, the object is stationary, or both. If a conductor is moving through a magnetic field generated by a "normal" source, like a chunk of magnetite held in your hand, then it will generate current unless it perfectly stays at the same flux density (in which case the field would be effectively uniform from the loop's perspective).

If by "moving but not leaving or entering" you meant moving but not crossing lines of flux, then the answer would be that no current is generated, because the EMF will remain balanced. In practice, this can't easily be done because the loop would have to move along a path with precision finer than the atoms inside it (unless you only want no measurable current, in which case the tolerance would be wider).

when a straight conductor is moved in and out of magnetic field,a potential difference is setup because when conductor is in magnetic field,force is exerted on free electrons and work is done by them (elctric potential) and when conductor is out of magnetic field,no force is acting on charges and so work done is zero.In this way,a potential difference is setup b/W ends of conductor.so emf is induced.when conductor is stationary or moving In constant magnetic flux,no emf is induced because there is no potential difference. But In case of electric generator,a coil is rotated in magnetic field.in horizontal position magnetic flux is minimum and is max. in vertical position of coil.when coil rotates inside magnetic field it moves from horizontal to vertical position.so, magnetic flux is changed and p.d. is setup due to which emf is induced as current flows from higher to lower potential.