AP Physics 1 Questions on Electric Field due to a Point Charge

📚 Quick Study Guide

• 💡 Electric Field: The electric field $\vec{E}$ at a point is the force per unit charge that a positive test charge would experience at that point: $\vec{E} = \frac{\vec{F}}{q}$.
• ⚡ Electric Field due to a Point Charge: The magnitude of the electric field $E$ due to a point charge $Q$ at a distance $r$ from the charge is given by: $E = k \frac{|Q|}{r^2}$, where $k = \frac{1}{4\pi\epsilon_0} \approx 8.99 \times 10^9 \text{ N m}^2/\text{C}^2$ is Coulomb's constant.
• 🧭 Direction of Electric Field: The electric field points radially outward from a positive charge and radially inward towards a negative charge.
• ➕ Superposition Principle: The electric field due to a group of point charges is the vector sum of the electric fields due to each individual charge: $\vec{E}_{\text{net}} = \vec{E}_1 + \vec{E}_2 + \dots$
• 📏 Units: Electric field is measured in Newtons per Coulomb (N/C) or Volts per meter (V/m).

🧪 Practice Quiz

1. A point charge of +2.0 μC is placed at the origin. What is the magnitude of the electric field at a point 3.0 m away on the x-axis?
   1. 5990 N/C
   2. 1997 N/C
   3. 2000 N/C
   4. 666 N/C
2. A −4.0 μC charge is located at (0, 0) m. What is the direction of the electric field at (2.0, 0) m?
   1. Along the positive x-axis
   2. Along the negative x-axis
   3. Along the positive y-axis
   4. Along the negative y-axis
3. Two point charges, +3.0 μC and −3.0 μC, are placed 0.2 m apart. What is the magnitude of the electric field at the midpoint between the charges?
   1. 1.35 × 10^6 N/C
   2. 2.70 × 10^6 N/C
   3. 0 N/C
   4. 6.75 × 10^5 N/C
4. A +5.0 μC charge is at (0, 0) m, and a +2.0 μC charge is at (4.0, 0) m. At what point on the x-axis is the electric field equal to zero?
   1. x = 2.35 m
   2. x = 6.83 m
   3. x = -4.0 m
   4. x = 0 m
5. What happens to the electric field strength if you double the distance from a point charge?
   1. It doubles
   2. It quadruples
   3. It is reduced by a factor of 2
   4. It is reduced by a factor of 4
6. A small object with a charge of $q = -8.0 \times 10^{-19}$ C is placed in an electric field of $E = 5.0 \times 10^2$ N/C. What is the electric force on the charge?
   1. 4.0 × 10^-16 N
   2. -4.0 × 10^-16 N
   3. 1.6 × 10^-21 N
   4. -1.6 × 10^-21 N
7. Two equal positive charges are separated by a distance d. At what point between the two charges is the electric field zero?
   1. d/4 from either charge
   2. d/2 from either charge
   3. At either charge
   4. The electric field is never zero between the charges