A flat slab of nonconducting material has thickness $2 d$, which is small compared to its height and breadth. Define the $x$ axis to be along the direction of the slab's thickness with the origin at the center of the slab. If the slab carries a volume charge density $\rho_{\mathrm{E}}(x)=-\rho_0$ in the region $-d \leq x<0$, and $\rho_{\mathrm{E}}(x)=+\rho_0$ in the region $0<x \leq+d$, determine the electric field $\overrightarrow{\mathbf{E}}$ regions $\text{(c) } -d \leq x<0$. Let $\rho_0$ be a positive constant.

Perform each of the following steps.
Use diagrams to show the critical region(or regions), and use the traditional method of hypothesis testing unless the $P$-value method is specified by your instructor.
Farm Sizes The average farm size in the United States is $444$ acres. A random sample of $40$ farms in Oregon indicated a mean size of $430$ acres, and the population standard deviation is $52$ acres. At $\alpha=0.05$, can it be concluded that the average farm in Oregon differs from the national mean? Use the $P$-value method.
a. State the hypotheses and identify the claim.

Perform each of the following steps.
Use diagrams to show the critical region(or regions), and use the traditional method of hypothesis testing unless the $P$-value method is specified by your instructor.
Sick Days in Bed A researcher wishes to see if the average number of sick days a worker takes per year is greater than $5.$ A random sample of $32$ workers at a large department store had a mean of $5.6.$ The standard deviation of the population is $1.2$. Is there enough evidence to support the researcher's claim at $\alpha=0.01$ ?
a. State the hypotheses and identify the claim.

Perform each of the following steps.
Use diagrams to show the critical region(or regions), and use the traditional method of hypothesis testing unless the $P$-value method is specified by your instructor.
Sick Days in Bed A researcher wishes to see if the average number of sick days a worker takes per year is greater than $5.$ A random sample of $32$ workers at a large department store had a mean of $5.6.$ The standard deviation of the population is $1.2$. Is there enough evidence to support the researcher's claim at $\alpha=0.01$ ?
b. Find the critical value(s) or use the $P$-value method.

Perform each of the following steps.
Use diagrams to show the critical region(or regions), and use the traditional method of hypothesis testing unless the $P$-value method is specified by your instructor.
Sick Days in Bed A researcher wishes to see if the average number of sick days a worker takes per year is greater than $5.$ A random sample of $32$ workers at a large department store had a mean of $5.6.$ The standard deviation of the population is $1.2$. Is there enough evidence to support the researcher's claim at $\alpha=0.01$ ?
c. Find the test value.

Perform each of the following steps.
Use diagrams to show the critical region(or regions), and use the traditional method of hypothesis testing unless the $P$-value method is specified by your instructor.
Sick Days in Bed A researcher wishes to see if the average number of sick days a worker takes per year is greater than $5.$ A random sample of $32$ workers at a large department store had a mean of $5.6.$ The standard deviation of the population is $1.2$. Is there enough evidence to support the researcher's claim at $\alpha=0.01$ ?
e. Summarize the results.

Perform each of the following steps.
Use diagrams to show the critical region(or regions), and use the traditional method of hypothesis testing unless the $P$-value method is specified by your instructor.
Sick Days in Bed A researcher wishes to see if the average number of sick days a worker takes per year is greater than $5.$ A random sample of $32$ workers at a large department store had a mean of $5.6.$ The standard deviation of the population is $1.2$. Is there enough evidence to support the researcher's claim at $\alpha=0.01$ ?
d. Make the decision.

A flat slab of nonconducting material has thickness $2 d$, which is small compared to its height and breadth. Define the $x$ axis to be along the direction of the slab's thickness with the origin at the center of the slab. If the slab carries a volume charge density $\rho_{\mathrm{E}}(x)=-\rho_0$ in the region $-d \leq x<0$, and $\rho_{\mathrm{E}}(x)=+\rho_0$ in the region $0<x \leq+d$, determine the electric field $\overrightarrow{\mathbf{E}}$ regions $\text{(b) } 0<x \leq+d$. Let $\rho_0$ be a positive constant.

The electric field $\overrightarrow{\mathbf{E}}$ is zero at all points on a closed surface; is there necessarily no net charge within the surface? If a surface encloses zero net charge, is the electric field necessarily zero at all points on the surface?

The electric field $\overrightarrow{\mathbf{E}}$ is zero at all points on a closed surface; is there necessarily no net charge within the surface? If a surface encloses zero net charge, is the electric field necessarily zero at all points on the surface?

A flat slab of nonconducting material carries a uniform charge per unit volume, $\rho_{\mathrm{E}}$. The slab has thickness $d$ which is small compared to the height and breadth of the slab. Determine the electric field as a function of $x$ (b) outside the slab (at distances much less than the slab's height or breadth). Take the origin at the center of the slab.

A flat slab of nonconducting material carries a uniform charge per unit volume, $\rho_{\mathrm{E}}$. The slab has thickness $d$ which is small compared to the height and breadth of the slab. Determine the electric field as a function of $x$ (a) inside the slab. Take the origin at the center of the slab.

Suppose two thin flat nonconducting plates measure $1.0 \mathrm{~m} \times 1.0 \mathrm{~m}$ and are separated by $5.0 \mathrm{~mm}$. They are oppositely charged with $\pm 25 \mu \mathrm{C}$. How much work would be required to move the plates from $5.0 \mathrm{~mm}$ apart to $1.00 \mathrm{~cm}$ apart?

Suppose two thin flat plates measure $1.0 \mathrm{~m} \times 1.0 \mathrm{~m}$ and are separated by $5.0 \mathrm{~mm}$. They are oppositely charged with $\pm 15 \mu \mathrm{C}$. (b) How much work would be required to move the plates from $5.0 \mathrm{~mm}$ apart to $1.00 \mathrm{~cm}$ apart?