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

Answer:

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

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:

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