Question

In a Cartesian coordinate system, there is a homogenous magnetic field B=0.25 T which directs into the x- direction. A piece of straight conducting wire of length 1m, which directs into the y-direction, moves at a constant speed v=0.23m/s in the z-direction. How large is the voltage between the two wire ends?​

Answer 1

Approximately
`0.0575\; {\rm V}`.

Step-by-step explanation:

Let
`B` denote the magnetic field strength. Let
`L` denote the length of this wire. Let
`v` denote the speed of this wire.

Let
`\theta` denote the angle between the magnetic field and the motion of this wire. To find the voltage (
`{\rm emf}`) induced in this wire, apply the formula:

`(\text{emf}) = B\, L\, (v\, \sin(\theta))`.

In this question, it is given that
`B = 0.25\; {\rm T}`,
`L = 1\; {\rm m}`, and
`v = 0.23\; {\rm m\cdot s^(-1)}`. Additionally,
`\theta = 90^(\circ)` since the magnetic field is perpendicular to the motion of the wire. Therefore, the voltage induced in this wire would be:

`\begin{aligned}(\text{emf}) &= B\, L\, (v\, \sin(\theta)) \\ &= (0.25\; {\rm T})\, (1\; {\rm m}) \, (0.23\; {\rm m\cdot s^(-1)}\, (\sin(90^(\circ)))) \\ &= 0.0575\; {\rm V}\end{aligned}`.