91Ó°ÊÓ

The magnetic field is.$\text{B}=\text{0.020T}$

One edge length of the block is $\text{L}=\text{25cm}$.

Speed of block along x is .${\text{v}}_{\text{x}}=\text{3.0m/s}$

Voltage along y is ${\text{V}}_{\text{y}}=\text{12mV}\left(\frac{{10}^{−3}\text{ }V}{1\text{ }mV}\right)=0.012\text{ }V$.

Voltage along z is ${\text{V}}_{\text{z}}=\text{18mV}\left(\frac{{10}^{−3}\text{ }V}{1\text{ }mV}\right)=0.018\text{ }V$

Voltage along x is ${\text{V}}_{\text{x}}=\text{0mV}$

Use the concept of voltage across two plates. Using the equation of voltage related to electric field and distance, find the distance.

Formulae are as follows:

$\text{E}=\frac{\text{V}}{\text{d}}$

Where E is the electric field, V is potential, and d is the distance between plates.

Length of block${\text{d}}_{\text{x}}$:

The distance along x is given${\text{d}}_{\text{x}}=\text{0.25m}\left(\frac{100\text{ }cm}{1\text{ }m}\right)$ .

Hence, the length of the block ${\text{d}}_{\text{x}}=\text{25cm}$.

Write the equation for electric field from electric force and magnetic force.

$qE=qvB$

$E=vB$

Using this value in the equation of voltage,

$vB=\frac{V}{d}$

Rearranging for d,

$d=\frac{V}{vB}$

It is given that v, d, and B are mutually perpendicular to each other.

Whenvelocity is along y, then the voltage is$\text{0.012V.}$

$d_y=\frac{V_y}{v_{y}B}$

$\begin{array}{l}{d}_y=\frac{0.012\text{ }V}{3.0\text{ }m/s×0.020\text{ }T}\\ d_y=0.20\text{ }m\left(\frac{100\text{ }cm}{1\text{ }m}\right)\\ d_y=20\text{ }cm\end{array}$

Hence, the length of the block .${\text{d}}_{\text{y}}=2\text{0cm}$

Length of block${\text{d}}_{\text{z}}$:

${\text{d}}_{\text{z}}=\frac{{\text{V}}_{\text{z}}}{{\text{v}}_{\text{z}}\text{B}}$

$\begin{array}{l}{\text{d}}_z=\frac{0.018\text{ }V}{3.0\text{ }m/s\text{ }×0.020\text{ }T}\\ {\text{d}}_z=0.30\text{ }m\left(\frac{100\text{ }cm}{1\text{ }m}\right)\\ {\text{d}}_z=30\text{ }cm\end{array}$

Hence, the length of the block ${\text{d}}_{\text{z}}=3\text{0cm}$

Therefore, use the concept of voltage across two plates to find the distances.