91影视

Figure 26-17 is the rectangular solid conductor of edge lengths L, 2L or 3L.

To explain the electrostatic force between the two charges, we assume that the charges create an electric field around them. The magnitude of electric field E set up by the electric charge q at a distance r is given as,

$\mathit{E}\mathbf{=}\frac{\mathbf{q}}{\mathbf{4}\mathbf{蟿}\mathbf{蟿}{\mathbf{蔚}}_{\mathbf{0}}{\mathbf{r}}^{\mathbf{2}}}$

The current density is electric current per unit cross-section area at a given point. The drift velocity of the electrons is the average velocity attained by the electrons.

We can use the formulae for the electric field, current density, current, and drift velocity to rank the given pairs of faces according to an electric field, current density, current, and the drift speed of the electrons.

Formulae:

The strength of the electric field,$E=\frac{V}{d}$ 鈥�(颈)

Here,E is the electric field,V is the potential difference, and is the separation between the two plates.

The current density of the material has a uniform current,$\mathrm{J}=\mathrm{IA}$ 鈥�(颈颈)

Here,J is the current density,I is current, andA is the area of the cross-section.

The drift velocity of electrons,$V_d=\frac{J}{ne}$ 鈥�(颈颈颈)

Here,$v_d$ is the drift velocity of the electrons,J is the current density,n is the number of electrons, and is the charge of electrons.

From equation (i), the electric field depends on the separation between the two faces of the conductor.

For left-right faces, the electric field through this face is given by,

$E_{LR}=\frac{V}{3L}$

For top 鈥揵ottom faces, the electric field through this face is given by,

$E_{TB}=\frac{V}{L}$

For front-back faces, the electric field through this face is given by,

$E_{FB}=\frac{V}{2L}$

From this, we can rank the pairs according to the magnitude of electric fields as,

$E_{TB}>E_{FB}>E_{LR}$

Current density depends on area here, because the charge flow will be same, considering equation (ii).

For left-right faces, the current density from this face is given by:

$$\begin{gathered} J_{LR}=I\left(2I脳L\right) \\ =2I{L}^2 \end{gathered}$$

For top 鈥揵ottom faces, the current density from this face is given by:

$$\begin{gathered} J_{TB}=I\left(2L脳3L\right) \\ =6I{L}^2 \end{gathered}$$

For front-back faces, the current density from this face is given by:

$$\begin{gathered} J_{FB}=I\left(L脳3L\right) \\ =3I{L}^2 \end{gathered}$$

From the above equations, we can rank the pairs according to the current density as,

$J_{TB}>J_{FB}>J_{LR}$

For left-right faces, the current through this face using equation (ii) and above values is given by:

$I_{LR}=J\left(2L^2\right)$

For top 鈥揵ottom faces, the current through this face using equation (ii) and above values is given by:

$I_{TB}=J\left(6L^2\right)$

For front-back faces, the current through this face using equation (ii) and above values is given by:

$I_{FB}=J\left(3L^2\right)$

From the above equations, we can rank the pairs according to the current as,

$I_{TB}>I_{FB}>I_{LR}$

Here, the drift velocity is directly proportional to the current density considering equation (iii).

From part b), we can write,$J_{TB}>J_{FB}>J_{LR}$

Hence, the rank value according to their speeds is $v_{dTB}>v_{dFB}>v_{dLR}$.