Electric Field from Point Charges

Zero Electric Field Locations

When multiple point charges are placed along a line, the electric field at any location is the vector sum of the fields due to each charge. The field is zero where the contributions from all charges cancel each other out.

• Direction of Electric Field: The field points towards a negative charge and away from a positive charge.

• Magnitude of Electric Field: The field due to a point charge is proportional to the charge and inversely proportional to the square of the distance:

• Zero Field Condition: For the field to be zero, the magnitudes of the fields from each charge must be equal and opposite in direction. This typically occurs outside the region between the charges, especially when the charges are unequal.

• Example: For charges and placed on a line, the zero field point is found where the field from cancels the field from . This is not between the charges, but on the side of the smaller charge.

Electric Field from Two Charges

Superposition Principle and Field Magnitude

The electric field at a point due to multiple charges is the vector sum of the fields from each charge. The arrangement and sign of the charges affect the direction and magnitude of the resulting field.

• Case A: Two positive charges and one negative charge are arranged around point P. The field at P is the sum of the vectors from each charge.

• Changing Charge Sign: If the negative charge is replaced by a positive charge of equal magnitude, the direction of its field contribution reverses, but the magnitude remains the same.

• Result: The magnitude of the electric field at P is largest when all charges are positive, as all field vectors point away from the charges and add constructively.

Electric Field from Three Charges

Symmetric Arrangements and Field Strength

When three charges are placed symmetrically around a point, the net electric field at the center depends on the relative magnitudes and directions of the individual fields.

• Example: One charge is placed at the top, and two charges are placed symmetrically at the bottom, all equidistant from the origin.

• Field Comparison: The field from the charge is twice as strong as that from each charge at the same distance.

• Direction: The net field from the two charges is along the vertical axis, while the charge contributes along the opposite direction. The net field is dominated by the charge.

Electric Dipoles

Definition and Properties

An electric dipole consists of two equal and opposite charges separated by a small distance. Dipoles are fundamental in molecular physics, such as in water molecules.

• Permanent Dipole: Exists in molecules like water, where the separation is fixed.

• Induced Dipole: Occurs when a neutral atom is polarized by an external electric field.

• Dipole Moment: The dipole moment vector has magnitude , where is the charge and is the separation distance. The direction is from negative to positive charge.

Electric Field of a Dipole

The electric field produced by a dipole at a point far from the dipole depends on the orientation of the point relative to the dipole axis.

• On the axis of the dipole:

• On the perpendicular bisector:

• Direction: The field points in the direction of the dipole moment vector .

Example Calculation: Water Molecule Dipole

Given a water molecule dipole moment , calculate the field at on the axis:

Plugging in values:

• Direction: Along the positive x-axis, same as .

Electric Field Lines

Properties and Interpretation

Electric field lines are a visual representation of the direction and strength of the electric field in space.

• Field Line Properties:

  • Field lines are continuous curves tangent to the electric field vectors.

  • Denser field lines indicate stronger electric field strength.

  • Field lines start on positive charges and end on negative charges.

  • Field lines never cross.

• Examples:

  • Field lines from a single positive charge radiate outward.

  • Field lines from a single negative charge converge inward.

  • Field lines from a dipole curve from the positive to the negative charge, showing the characteristic pattern of a dipole field.

Table: Comparison of Electric Field Lines

Applications and Safety

Lightning and Electric Fields

Large electric fields can occur during thunderstorms due to charge separation, which can be hazardous. It is important to seek shelter during lightning storms.

Additional info: The notes cover fundamental concepts in electrostatics, including the calculation and visualization of electric fields from point charges and dipoles, and their real-world implications.