The Field Beside a Finite Rod: Two Components, Two End Angles

Work each one out before you check it. Every question has a scratch pad and a calculator.

1. Question 1

   A rod lies on the $x$-axis from $x_1 = -0.15\ \text{m}$ to $x_2 = 0.45\ \text{m}$, and $P = (0,\ 0.15\ \text{m})$. Find the end angles, measured from the $y$-axis (positive toward $+x$), in degrees to one decimal place.

   $\theta_1 =$°

   $\theta_2 =$°

   Check

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2. Question 2

   Use $k_e = 8.99\times10^{9}\ \text{N}\,\text{m}^2/\text{C}^2$. A rod with $\lambda = 2.0\ \text{nC/m}$ lies on the $x$-axis from $x_1 = -0.10\ \text{m}$ to $x_2 = 0.30\ \text{m}$. Find $E_y$ at $P = (0,\ 0.20\ \text{m})$, in N/C to three significant figures.

   $E_y =$N/C

   Check

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3. Question 3

   Use $k_e = 8.99\times10^{9}\ \text{N}\,\text{m}^2/\text{C}^2$. A rod with $\lambda = 3.0\ \text{nC/m}$ lies on the $x$-axis from $x_1 = 0.20\ \text{m}$ to $x_2 = 0.50\ \text{m}$. Find $E_x$ (with its sign) at $P = (0,\ 0.20\ \text{m})$, in N/C to three significant figures.

   $E_x =$N/C

   Check

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4. Question 4

   Use $k_e = 8.99\times10^{9}\ \text{N}\,\text{m}^2/\text{C}^2$. A rod with $\lambda = 4.0\ \text{nC/m}$ lies on the $x$-axis from $x = 0.20\ \text{m}$ to $x = 0.50\ \text{m}$. Find $E_x$ (with its sign) at the origin, in N/C to three significant figures.

   $E_x =$N/C

   Check

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5. Question 5

   Use $k_e = 8.99\times10^{9}\ \text{N}\,\text{m}^2/\text{C}^2$. A very long rod with $\lambda = 2.5\ \text{nC/m}$ starts at the origin and runs along the $+x$ axis without end. Find $E_x$ and $E_y$ (with their signs) at $P = (0,\ 5.0\ \text{cm})$, in N/C to three significant figures.

   $E_x =$N/C

   $E_y =$N/C

   Check

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