The Six-Step Recipe for Continuous Charge Fields

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

1. Question 1

   A disk carries $\sigma = 5.0\ \mu\text{C/m}^2$. Find the charge $dq$ on the thin ring of the disk at radius $r' = 2.0\ \text{cm}$ with width $dr' = 0.10\ \text{mm}$, in picocoulombs to three significant figures.

   $dq =$pC

   Check

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2. Question 2

   A thin disk of radius $R$ carries a total charge $Q$ spread uniformly over it. On its axis at $z = 2R$, what fraction of the point-charge value $k_eQ/z^2$ is the disk's actual field $E_z$? Give it to three significant figures.

   $E_z \big/ \dfrac{k_eQ}{z^2} =$

   Check

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3. Question 3

   Use $k_e = 8.99\times10^{9}\ \text{N}\,\text{m}^2/\text{C}^2$. A ring of radius $R = 0.090\ \text{m}$ carries $Q = 4.0\ \text{nC}$. Find $E_z$ on its axis at $z = 0.12\ \text{m}$, in N/C to three significant figures.

   $E_z =$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 line charge of length $\ell = 0.30\ \text{m}$ carries $\lambda = 2.0\ \text{nC/m}$. Find the field on its perpendicular bisector at $y = 0.20\ \text{m}$ from its midpoint, in N/C to three significant figures.

   $E_y =$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 disk of radius $R = 4.0\ \text{cm}$ carries $\sigma = 1.0\ \mu\text{C/m}^2$. Find $E_z$ on its axis at $z = 3.0\ \text{cm}$, in N/C to three significant figures.

   $E_z =$N/C

   Check

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