Electric charges

Electric Force and Coulomb's Law

Introduction to Electric Force

• Electric force is described by Coulomb's Law.

• Similar to gravitational force where massive objects attract each other, charged particles exert forces on each other.

  • Positive Charges: Repulsive force (forces away from each other).

  • Negative Charges: Repulsive force (forces away from each other).

  • Mixed Charges (Positive and Negative): Attractive force (forces towards each other).

Principles of Electric Force

• Newton's Third Law: The force exerted by charged particles is equal in magnitude and opposite in direction, similar to gravitational forces.

Coulomb's Law Formula

• The electric force between two charged particles, represented as q1 and q2, is given by:

  • Electric Force (F) = (1 / (4 * π * ε₀)) * (q1 * q2) / r² * r̂

    • where:

      • ε₀: permittivity of free space, approximately equal to 8.85 x 10^(-12) C²/N·m² or 9 x 10^9 N·m²/C² for calculations.

      • r: distance between the charges, and r̂ is the unit vector in the direction from one charge to the other.

Charge Values

• Charge is measured in Coulombs (C).

  • Charge of a proton: +e = +1.6 x 10^(-19) C

  • Charge of an electron: -e = -1.6 x 10^(-19) C

  • Alpha Particle: Contains 2 protons and has a charge of +2e.

Example Calculation

• Example: Calculate the force on an alpha particle by a gold nucleus.

• Suppose the alpha particle is at coordinates (-5, 3) and the gold nucleus at (1, 0):

  • Determine r vector: r = position of alpha particle - position of gold nucleus.

  • Calculate force using Coulomb's Law: Plug in values of charges and distance to find the force.

Key Takeaways From Example

• The direction of the force is based on the nature of the charges:

  • Forces due to like charges (both positive/negative) are in the direction of r (repulsion).

  • Forces due to unlike charges (one positive, one negative) are towards each other (attraction).

• When calculating vector quantities in physics (such as forces), it is useful to compute an easier component, often the x-component.

Comparative Force Examples

• Electric force magnitude depends on both interacting charges:

  • Greater charge on one particle results in greater force upon the other particle.

  • Example 1: Force on an alpha particle compared to a gold nucleus.

  • If comparing to a proton (with half the charge), the force on the proton is also half as strong compared to the alpha particle due to the lower charge.

Inverse Square Law

• Electric force like gravitational force follows an inverse square law:

  • Relationship: Doubling the distance decreases the force by a quarter (1/4).

Final Thoughts on Electric Forces

• Draw diagrams for understanding forces acting on a central body.

• Factor in both the distance and charge interactions when calculating resultant forces.

Application in Tests and Practice

• For tests, focus calculations to the x-component of vectors to save time, unless circumstances require further calculation of y-components.