Section 9.1: Electric Forces and Electric Field
Electric forces arise between charged objects. The magnitude of the force between two point charges is given by Coulomb's Law.
\[
F = k \frac{|q_1 q_2|}{r^2}
\]
where:
\( F \) = magnitude of electric force (N)
\( q_1, q_2 \) = charges (C)
\( r \) = distance between charges (m)
\( k = 8.99 \times 10^9 \, \text{N·m²/C²} \)
\( F \) = magnitude of electric force (N)
\( q_1, q_2 \) = charges (C)
\( r \) = distance between charges (m)
\( k = 8.99 \times 10^9 \, \text{N·m²/C²} \)
The electric field is defined as the force per unit charge experienced by a small test charge:
\[
\vec{E} = \frac{\vec{F}}{q_0}
\]
where:
\( \vec{E} \) = electric field (N/C)
\( \vec{F} \) = force on test charge (N)
\( q_0 \) = test charge (C)
\( \vec{E} \) = electric field (N/C)
\( \vec{F} \) = force on test charge (N)
\( q_0 \) = test charge (C)
Example 1: Force Between Charges
Two charges of 3 μC and 5 μC are 0.2 m apart. Find the magnitude of the electric force between them.
\( F = k \frac{|q_1 q_2|}{r^2} = 8.99\times10^9 \frac{(3\times10^{-6})(5\times10^{-6})}{0.2^2} \approx 3.37 \, \text{N} \)
Example 2: Electric Field
A test charge of 2 μC experiences a force of 0.01 N. Find the electric field at that point.
\( E = F/q_0 = 0.01 / (2 \times 10^{-6}) = 5000 \, \text{N/C} \)
Practice Problems
- Two point charges, 1 μC and 2 μC, are separated by 0.1 m. Calculate the force between them.
- A 5 μC charge experiences a 0.02 N force. Determine the electric field at the location of the charge.
- If two like charges are separated by 0.5 m and experience a force of 10 N, find the magnitude of each charge.
- A 3 μC charge is placed in a uniform electric field of 2000 N/C. Find the force on the charge.
- Three point charges lie in a straight line: 1 μC, -2 μC, 3 μC, separated by 0.3 m each. Calculate the net force on the middle charge.