# What should be the direction of motion of a conductor in a magnetic field to produce motional emf?

Physics Asked by Swami on December 21, 2020

Here’s the textbook question: Twelve wires of equal length ‘l’ are connected to form a skeleton cube which moves with constant velocity v perpendicular to the magnetic field B. What will be the induced emf in each arm of the cube? As per my understanding, motional emf is produced in a conductor that moves in a direction perpendicular to the magnetic field. Hence, each arm should develop a motional emf.

The book says – “Emf is produced only in the arms that are perpendicular to both $V$ & $B$. Thus, only EH, FG, AD, BC produce a motional emf, $epsilon= BLV$ “

Timaeus succinctly gives the fundamental Physics. But it's worth remembering Faraday's empirical rule: an emf is induced in a conductor when it cuts lines of magnetic flux. In your diagram lines of magnetic flux run from left to right. As the skeleton cube moves 'upwards', only EH, FG, AD, BC cut these lines.

We can easily understand why no emfs are induced in AB, DC, EF, HG (the edges parallel to the field). The magnetic Lorentz force on the free electrons in these conductors is in the direction CB (or out of the page) so the free electrons are urged transversely to their conductors rather than in either direction along the conductors, so there is no emf between the ends of the conductors.

It's a similar case for the vertical edges, ED, HA, GB, FC. Again the magnetic Lorentz force on the free electrons is out of the page and transverse to the conductors.

Only when the alignment of the conductors is into and out of the page is the Lorentz force on the free electrons aligned along the conductors.

Answered by Philip Wood on December 21, 2020

An EMF requires the force per unit charge of the source (in our case $vec{v}timesvec{B}$) and then you take the scalar product of that with the vector in the direction of the circuit element (in our case $dvec{s}$).

If either $vec{v}$ or $vec{B}$ (or both!) point in the same direction as $dvec{s}$ then the cross product $vec{v}timesvec{B}$ will be orthogonal to $dvec{s}$, and so no EMF.

Answered by Timaeus on December 21, 2020

let us consider the branch EH velocity is directed +y and magnetic field is along +x so by definition F=qvXB positive charge accumulates at E thus giving it Some potential. point to note here net emf produced here will be zero as magnetic field is constant throughout so dφ/dt equals zero. other wires Example DC also produces potential but in a direction that is in the direction of width and not length so ΔL=0 aprox so transverse emf (SEE halls effect) will be almost zero even though it is not exactly zero. Same thing will happen to the wire DE say. Transverse EMF is produced so ΔL=0 aprox.

Answered by Einstein'sLover on December 21, 2020

## Related Questions

### UV catastrophe and Equipartition Theorem absurdity

1  Asked on June 18, 2021 by lamplamp

### How does making harmonics work on a guitar?

2  Asked on June 18, 2021

### Induced gravitation action

1  Asked on June 18, 2021

### 3 x 2 or 6 x 2 Surface Reconstruction

1  Asked on June 18, 2021 by juststartedstudying

### Electric potential/gravitational potential

1  Asked on June 18, 2021

### Why do two objects at distance of closest approach have equal velocity?

2  Asked on June 18, 2021

### References for effective viscosity experiments

0  Asked on June 18, 2021 by velobos

### Does the Kalman filter incorporate a Heisenberg-like uncertainty principle?

0  Asked on June 18, 2021

### Significance of wave number?

3  Asked on June 18, 2021 by anil-kamat

### Does the Earth emit gravitational waves?

2  Asked on June 18, 2021 by anubhav-goel

### How much time does a moving observer measure me measuring?

1  Asked on June 18, 2021

### Factoring the Laplace operator $Delta$ in dimensions $D geq 3$

1  Asked on June 18, 2021 by gsuer

### Why does the fine-structure constant $α$ have the value it does?

3  Asked on June 18, 2021 by magix

### Particle on a moving wedge: Reaction Force

1  Asked on June 18, 2021

### Does sputtering Au on top of PEDOT:PSS thin film alter its properties?

0  Asked on June 18, 2021 by preposteroustomato

### On generators of $SO(2)$

1  Asked on June 18, 2021

### Are protons bigger than electrons?

5  Asked on June 18, 2021

### Particle in a cylinder with a spring, sign convention in potential energy (Lagrangian multipliers)

1  Asked on June 18, 2021

### Does cooking food in pressure cooker depend on outside pressure

2  Asked on June 18, 2021 by thejas-suresh

### How to apply Feynman rules of counterterms to calculate amplitudes?

1  Asked on June 17, 2021