Electric Field Solved Examples: Step-by-Step Solutions for Physics Students

📚 Quick Study Guide

• ⚡ The electric field ($\vec{E}$) is a vector field that exists at every point in space. It exerts a force on any charged object within it.
• 📏 The electric field due to a point charge $q$ at a distance $r$ is given by: $\vec{E} = k \frac{q}{r^2} \hat{r}$, where $k = 8.99 \times 10^9 \text{ N m}^2/\text{C}^2$ is Coulomb's constant and $\hat{r}$ is the unit vector pointing from the charge to the point of interest.
• ➕ The electric field due to multiple point charges is the vector sum of the electric fields due to each individual charge (Superposition Principle). $\vec{E}_{\text{net}} = \vec{E}_1 + \vec{E}_2 + ...$
• 📊 Electric field lines are a visual representation of the electric field. They point in the direction of the electric field vector at each point. The density of field lines is proportional to the magnitude of the electric field.
• 💡 The electric force on a charge $q$ in an electric field $\vec{E}$ is given by $\vec{F} = q\vec{E}$.

Practice Quiz

1. A positive charge of $2 \mu C$ is placed in an electric field of $500 \text{ N/C}$ directed to the right. What is the magnitude and direction of the electric force on the charge?
   1. $1 \times 10^{-3} \text{ N}$ to the left
   2. $1 \times 10^{-3} \text{ N}$ to the right
   3. $2.5 \times 10^{-3} \text{ N}$ to the left
   4. $2.5 \times 10^{-3} \text{ N}$ to the right
2. What is the electric field at a distance of $0.5 \text{ m}$ from a point charge of $5 \times 10^{-6} \text{ C}$?
   1. $9 \times 10^{4} \text{ N/C}$
   2. $1.8 \times 10^{5} \text{ N/C}$
   3. $9 \times 10^{5} \text{ N/C}$
   4. $1.8 \times 10^{6} \text{ N/C}$
3. Two charges, $+q$ and $-q$, are separated by a distance $d$. What is the electric field at the midpoint between the two charges?
   1. 0
   2. $\frac{kq}{d^2}$
   3. $\frac{2kq}{d^2}$
   4. $\frac{4kq}{d^2}$
4. A uniform electric field of magnitude $300 \text{ N/C}$ is directed along the positive y-axis. A charge of $-3 \mu C$ is placed in this field. What is the electric force acting on the charge?
   1. $9 \times 10^{-4} \text{ N}$ along the positive y-axis
   2. $9 \times 10^{-4} \text{ N}$ along the negative y-axis
   3. $1 \times 10^{-6} \text{ N}$ along the positive y-axis
   4. $1 \times 10^{-6} \text{ N}$ along the negative y-axis
5. The electric field lines are closer to each other at point A than at point B. What does this indicate about the electric field strength at these points?
   1. The electric field strength is the same at both points.
   2. The electric field strength is stronger at point A than at point B.
   3. The electric field strength is weaker at point A than at point B.
   4. The electric field is zero at point A.
6. What is the net electric field at the center of a square with equal positive charges at each corner?
   1. The electric field is non-zero and points towards one of the corners.
   2. The electric field is non-zero and points towards the center of one of the sides.
   3. The electric field is zero.
   4. The electric field is infinite.
7. A charged particle is moving in an electric field. If the particle's kinetic energy is increasing, what can you conclude about the work done by the electric field on the particle?
   1. The electric field is doing negative work on the particle.
   2. The electric field is doing positive work on the particle.
   3. The electric field is doing zero work on the particle.
   4. The work done by the electric field cannot be determined from the given information.