91影视

The given data can be listed below as-

• The given starting position of the rod is,$I_1=A$
• The given end position of the rod is,$I_2=-A$
• The location of the electric field is,
• The charge of the rod is,$E=-Q$

The electric field is a region which helps a charged particle to induce force on another charged particle.

The equation of the charge per unit length is expressed as,

$q=\frac{E}{a}$鈥�(1)

Here,$E$ is the charge of the rod and is the total area of the rod.

(a)

Rewrite equation (1) as follows,

$q=\frac{E}{I_1+I_2}$

Here,$I_1$ and$I_2$ are the area at the starting point and end point respectively

For$E=-Q,I_1=A$,and$I_2=-A$.

$$\begin{gathered} q=\frac{-Q}{A-\left(-A\right)} \\ =\frac{-Q}{2A} \end{gathered}$$鈥�(2)

Thus, the change per unit area of the rod is$\frac{-Q}{2A}$.

(b)

The small amount of the charge$dQ$on small piece of length$dx$, is expressed by using equation (2) as follows,

$$\begin{gathered} dq=\frac{-Q}{2A}dx \\ =-\frac{Qdx}{2A} \end{gathered}$$鈥�(3)

Thus, the amount of the charge $dQ$on the small piece of length $dx$is$-\frac{Qdx}{2A}$$-\frac{Qdx}{2A}$.

(c)

As the electric field is at the locationand as it is in the$xy$ plane, so there will not be any$z$ coordinate. However, as the length of the$-x$ rod starts from the direction, hence, the vector fromthe source to the observation locationis .

Thus, the vector from this source to the observation location is.

(d)

The equation of the distance of the source to the observation location is expressed as,

$d=\sqrt{a^2+b^2+c^2}$

Here,$a$ , $b$and $c$are the values of the$x$ ,$y$ , and$z$ coordinate respectively.

For $a=-x$and$b=y$,

$$\begin{gathered} d=\sqrt{{\left(-x\right)}^2+y^2} \\ =\sqrt{x^2+y^2} \end{gathered}$$

Thus, the distance from the source to the observation location is$\sqrt{x^2+y^2}$.

(e)

According to the equation (3), as $dx$is the change of the length, then if an integral is set up to find the electric field at the observation location due to the entire rod, then the integration variable will be$x$ .

Thus, the integration variable will be $x$.