Question

a. What are the $x$- and $y$-components of vector $\overrightarrow{E}$shown in FIGURE EX3.3 in terms of the angle $\theta$and the magnitude $E$?

b. For the same vector, what are the $x$- and $y$-components in terms of the angle $\varphi$and the magnitude$E?$

Short answer

(a) The component is $E_x=E\sin \theta and{E}_y=E\cos \theta .$

(b) The components arerole="math" localid="1649187984859" $E_x=E\cos \varphi and{E}_y=E\sin \varphi .$

Step-by-step solution

Part (a) Step 1. Given information

The given figure is,

We need to write the $x$- and $y$- component of the vector$\overrightarrow{E}$shown in terms of the angle$\theta$and magnitude$E.$

Step 2. Solution

The component vectors are parallel to the $xandy$axis. localid="1649187951196" $\overrightarrow{E}=\overrightarrow{E_x}+\overrightarrow{E_y}.$

From the figure,

$E_x=E\sin \theta and{E}_y=E\cos \theta .$

Part (b) Step 1. Given information

The given figure is,

We need to write the $x$- and $y$- component of the vector $\overrightarrow{E}$ shown in terms of the angle $\varphi$ and magnitude$E.$

Step 2. Solution

The component vectors are parallel to the $xandy$axis.

$\overrightarrow{E}=\overrightarrow{E_x}+\overrightarrow{E_y}.$

In the figure,

$E_x=E\cos \varphi and{E}_y=E\sin \varphi .$