Section 2.9: Relation Between Electric Field and Force
The electric field is defined as the force per unit charge. It provides a way to describe how charges interact in space without referring directly to other charges.
Definition:
\[ \vec{E} = \frac{\vec{F}}{q} \] where \( \vec{F} \) is the force experienced by a test charge \( q \), and \( \vec{E} \) is the resulting electric field at that point.
Implications:
- Electric field allows calculation of force on any charge: \( \vec{F} = q\vec{E} \).
- Superposition applies: fields from multiple sources add vectorially.
- Direction of \( \vec{E} \) is the direction of force on a positive test charge.
Example 1
A point charge \( q = +2 \, \mu C \) is placed in an electric field \( \vec{E} = 5 \hat{i} \, \text{N/C} \). Find the force on the charge.
\[ \vec{F} = q \vec{E} = (2 \times 10^{-6}) (5 \hat{i}) = 1.0 \times 10^{-5} \hat{i} \, \text{N} \]
The force points in the same direction as the field since the charge is positive.
Practice Problems
- Define electric field in words and relate it to force.
- Calculate the force on a \( -3 \, \mu C \) charge in a uniform field \( \vec{E} = 4 \hat{j} \, \text{N/C} \).
- Two point charges are separated by distance \( r \). Express the electric field due to one at the location of the other.
- Explain how superposition affects the net force on a test charge in multiple fields.
- Discuss the direction of force for positive vs negative test charges in a given field.