Charging and Polarization

Charging a Polarized Electroscope

An electroscope is a device used to detect electric charge. When a charged rod is brought near the disk of an electroscope without touching it, the electroscope becomes polarized. If the rod briefly touches the end of the post and is then removed, the state of the electroscope changes due to the transfer of charge.

• Polarization: The redistribution of charges within the electroscope due to the presence of a nearby charged object.

• Charging by Induction: The process by which a neutral object acquires a net charge without direct contact, typically by grounding while a charged object is nearby.

• Result: After the process, the electroscope may have an excess of positive or negative charge depending on the nature of the rod and the steps taken.

• Example: If a negatively charged rod is used and the electroscope is grounded while the rod is near, electrons are repelled, leaving the electroscope positively charged after the rod is removed.

Coulomb's Law

Fundamental Concepts

Coulomb's law describes the force between two point charges. The magnitude of the charge of an electron or proton is known as the fundamental charge, denoted as C.

• Electrostatic Constant: N·m2·C-2

• Coulomb's Law Equation:

• Direction: The force acts along the line joining the two charges. It is repulsive for like charges and attractive for opposite charges.

• Newton's Third Law: The force exerted by on is equal in magnitude and opposite in direction to the force exerted by on .

Examples and Applications

• Example: Two charges, and , separated by a distance , experience a force calculated using Coulomb's law.

• Application: Used to determine the behavior of charged particles in fields, such as in atomic and molecular physics.

Vector Nature of Electric Force

Direction and Magnitude

The electric force between two charges is a vector quantity, having both magnitude and direction. The direction depends on the sign of the charges.

• Like Charges: Repel each other; force vectors point away from each other.

• Opposite Charges: Attract each other; force vectors point toward each other.

• Newton's Third Law Pair: Forces are equal in magnitude and opposite in direction.

Calculating Electric Force: Worked Example

Example Calculation

Given C at the origin and C at , calculate the electric force on .

• Distance Calculation (Pythagorean theorem):

• Force Magnitude:

• Direction: Since the charges are opposite, the force is attractive.

Components of Electric Force

• x-component:

• y-component:

• Sign Convention: The direction of the force components depends on the relative positions and signs of the charges.

Coulomb's Law for Multiple Charges

Superposition Principle

When more than two charges are present, the net electric force on a given charge is the vector sum of the forces exerted by all other charges.

• Net Force Equation:

• Application: Used to analyze systems with multiple point charges, such as molecules or charged conductors.

Electric Force in Linear Arrangements

Charges in Line: Net Force Analysis

Consider a central charge with two other charges placed at equal distances above and below it. The net force on the central charge depends on the signs of the surrounding charges.

• Case 1: Surrounding charges have opposite signs.

• Case 2: Surrounding charges are both positive.

• Direction: If is negative, the direction of the force arrows reverses.

• Net Force: If the forces are in the same direction, the net force is larger than in the case where they are in opposite directions (which can result in zero net force).

• Answer to this problem is Case 1

Summary Table: Coulomb's Law and Electric Force

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