Electric force on a charge in an electric field: Definition and explanation

📚 Definition of Electric Force on a Charge in an Electric Field

The electric force on a charge in an electric field is the force experienced by a charged particle due to the presence of the electric field. This force is directly proportional to the magnitude of the charge and the strength of the electric field. Essentially, the electric field exerts a push or pull on the charge.

🧲 Formula and Explanation

The electric force ($F$) on a charge ($q$) in an electric field ($E$) is given by the following formula:

$F = qE$

• 🔍 F: Electric Force (measured in Newtons, N)
• ⚡ q: Magnitude of the Charge (measured in Coulombs, C)
• 🌐 E: Electric Field Strength (measured in Newtons per Coulomb, N/C)

Key Points:

• ➕ If $q$ is positive, the electric force $F$ is in the same direction as the electric field $E$.
• ➖ If $q$ is negative, the electric force $F$ is in the opposite direction of the electric field $E$.
• 💪 The stronger the electric field ($E$) or the larger the charge ($q$), the greater the force ($F$).

💡 Example Problem

A charge of +2 $\mu$C (micro Coulombs) is placed in a uniform electric field of 500 N/C directed to the right. What is the electric force on the charge?

Solution:

First, convert the charge to Coulombs:

$q = 2 \mu C = 2 \times 10^{-6} C$

Then, use the formula $F = qE$:

$F = (2 \times 10^{-6} C)(500 N/C) = 1 \times 10^{-3} N$

The electric force on the charge is $1 \times 10^{-3} N$ to the right.

📝 Factors Affecting Electric Force

• 📏 Magnitude of Charge: The greater the charge, the greater the force.
• 💪 Electric Field Strength: A stronger electric field results in a stronger force.
• 📍 Location: The electric field strength can vary from point to point, affecting the force experienced by the charge at different locations.

🛡️ Shielding and Superposition

The electric field and thus the force can be affected by:

• 🚧 Shielding: Conductors can shield electric fields. If a charge is placed inside a hollow conductor, the electric field inside can be zero, resulting in zero force.
• ➕ Superposition: When multiple charges are present, the total electric field at a point is the vector sum of the electric fields due to each individual charge. The force on a test charge is then determined by this net electric field.

⚗️ Experimental Verification

Experiments can be conducted to verify the relationship between electric force, charge, and electric field. These experiments often involve:

• 🧪 Millikan's Oil Drop Experiment: Demonstrates the quantization of electric charge and measures the electric force on charged oil droplets suspended in an electric field.
• 🔬 Cathode Ray Tube (CRT): Electrons are deflected by electric fields, allowing for the visualization and measurement of electric forces.

📚 Real-World Applications

• 📺 Electronics: Electric forces are fundamental to the operation of electronic devices, such as transistors and capacitors.
• ⚡ Electrostatic Painting: Charged paint particles are attracted to a grounded object, creating a uniform coating due to electric forces.
• 🖨️ Laser Printers: Electric fields are used to control the deposition of toner on a drum, creating an image that is then transferred to paper.

🧪 Practice Quiz

Test your understanding with these practice questions:

1. What is the electric force on a -3 $\mu$C charge in an electric field of 200 N/C directed to the left?
2. A charge experiences a force of 4 x 10⁻³ N in an electric field of 800 N/C. What is the magnitude of the charge?
3. If the electric field strength is doubled, what happens to the electric force on a charge?