8.4 Electric Fields of Charge Distributions

• The total electric field due to a group of point charges is the vector sum of the individual
• In the electric field formula, k</latex> is known as Coulomb's constant
• Steps to find the total electric field at a point due to multiple charges

  1️⃣ Calculate individual electric fields

  2️⃣ Sum the fields vectorially
• The principle of superposition applies only to electric fields and not to gravitational fields.


  True
• What is the principle of superposition for electric fields?

  Vector sum of fields
• What is the approximate value of the electric field due to a charge of + 8 \text{ nC}</latex> at a distance of $2 \text{ m}$?


  18 N / C
• The electric field due to a point charge decreases with the square of the distance.


  True
• The principle of superposition allows for the calculation of the total electric field at a point due to multiple charges.


  True
• The electric field due to a point charge is calculated using the formula $\vec{E} =$$\frac{k q}{r^{2}} \hat{r}$.


  True
• The principle of superposition for electric fields is equivalent to adding the electric potentials due to individual charges.

  False
• What is the formula for the total electric field due to a group of point charges $q_{1}, q_{2}, \dots, q_{n}$ at positions $\vec{r}_{1}, \vec{r}_{2}, \dots, \vec{r}_{n}$?


  $\vec{E}_{\text{total}} =$$\sum_{i = 1}^{n} \frac{k q_{i}}{|\vec{r} - \vec{r}_{i}|^{2}} \hat{r}_{i}$
• What is the formula for the electric field $\vec{E}$ due to a line charge distribution with linear charge density $\lambda$?


  $\vec{E} =$$\int \frac{k dQ}{r^{2}} \hat{r}$
• The electric field due to a surface charge distribution is calculated by integrating over the entire surface


  True
• In the surface charge formula, $dQ =$$\sigma dA$ represents the differential charge element
• The surface charge density $\sigma$ is defined as the charge per unit area on a surface.


  True
• Match the parameter with its description:

  R ↔️ Radius of disk

  \sigma ↔️ Surface charge density

  z ↔️ Distance from disk
• The principle of superposition for electric fields states that the total field is the vector sum of the individual fields
• The electric field due to a point charge $q$ at a distance $r$ is given by \frac{k q}{r^{2}}
• The unit of charge is the coulomb.
• What is the linear charge density $\lambda$ for a line charge distribution?


  $\lambda =$$\frac{Q}{L}$
• Match the concept with its description:

  Point Charge ↔️ Charge concentrated at a single location

  Line Charge ↔️ Charge distributed along a line

  Superposition ↔️ Sum of electric fields from multiple charges
• What is the approximate value of Coulomb's constant $k$?


  $8.987 \times 10^{9} \text{ N m}^{2} \text{C}^{ - 2}$
• The integral to find the electric field of a uniformly charged rod is $\int_{0}^{L} \frac{k \lambda dl}{(x + d)^{2}} \hat{i}$


  True
• Surface charge density is defined as charge per unit area
• What is the principle of superposition for electric fields?

  Vector sum of individual fields
• What is the formula for the electric field due to a point charge?

  $\vec{E} =$$\frac{k q}{r^{2}} \hat{r}$
• How do you calculate the total electric field at a point due to two charges using superposition?

  Vector sum of individual fields
• What is the direction of the unit vector $\hat{r}$ in the electric field formula?


  From charge to point of interest
• The electric field due to a point charge decreases with the square of the distance
• The electric field measures the electric force per unit charge.


  True
• What is the approximate value of the electric field due to a charge of $- 6 \text{ nC}$ at a distance of $3 \text{ m}$?


  6 N / C
• What is the mathematical expression for the principle of superposition for electric fields?

  $\vec{E}_{\text{total}} =$$\vec{E}_{1} +$$\vec{E}_{2} +$$\dots +$$\vec{E}_{n}$
• What does the principle of superposition for electric fields state?

  Vector sum of fields
• What is the second step in calculating the total electric field due to multiple charges?

  Add vectorially
• The principle of superposition allows us to calculate the electric field due to multiple charges by summing the individual electric fields vectorially
• The electric field due to a line charge distribution is calculated by integrating the contributions of small charge segments along the line


  True
• What is the electric field due to a uniformly charged straight wire of length $L$ with linear charge density $\lambda$ at a perpendicular distance $x$ from the center of the wire?


  $\vec{E} =$$\frac{2k \lambda}{x} \sin(\theta)$
• What is the general formula for calculating the electric field due to a surface charge distribution?

  $\vec{E} =$$\iint \frac{k dQ}{r^{2}} \hat{r}$
• The electric field along the axis of symmetry of a uniformly charged disk is given by 2 \pi k \sigma
• The electric field inside a uniformly charged sphere is proportional to the distance from its center.

  True