plumb line

Examples of plumb line in the following topics:

• Locating the Center of Mass

  • In two dimensions: An experimental method for locating the center of mass is to suspend the object from two locations and to drop plumb lines from the suspension points.
  • The intersection of the two lines is the center of mass .
  • Suspend the object from two locations and to drop plumb lines from the suspension points.
  • The intersection of the two lines is the center of mass.

• Eratosthenes' Experiment

  • By Earth's gravity, the mass hung straight down; the line of the string established a "vertical" at that geographic location.
  • To measure the angle of incident sunlight there Eratosthenes lowered a plumb bob suspended by a string deep into a well.

• Equipotential Lines

  • This means that if a charge is at any point on a given equipotential line, no work will be required to move it from one point to another on that same line.
  • An isolated point charge Q with its electric field lines (blue) and equipotential lines (green)
  • When charges are lined up and continuous on conducting plates, equipotential lines are straight between them.
  • The only exception is a curving of the lines near the edges of the conductor plates.
  • Describe the shape of the equipotential lines for several charge configurations

• Magnetic Field Lines

  • Magnetic field lines are like the contour lines (constant altitude) on a topographic map in that they represent something continuous, and a different mapping scale would show more or fewer lines.
  • Various phenomena have the effect of "displaying" magnetic field lines as though the field lines are physical phenomena.
  • For example, iron filings placed in a magnetic field line up to form lines that correspond to "field lines. " Magnetic fields' lines are also visually displayed in polar auroras, in which plasma particle dipole interactions create visible streaks of light that line up with the local direction of Earth's magnetic field.
  • We use magnetic field lines to represent the field (the lines are a pictorial tool, not a physical entity in and of themselves).
  • It is exactly proportional to the number of lines per unit area perpendicular to the lines (called the areal density).

• Electric Field Lines: Multiple Charges

  • Thus far, we have looked at electric field lines pertaining to isolated point charges.
  • One could also choose to connect 3, 6, and 9 field lines, respectively, to q1, q2, and q3; what matters is that the number of lines are related to the charge values by the same proportionality constant.
  • Field lines should always point away from positive charges and towards negative charge.
  • If there are opposite charges in consideration, connect one to the other with field lines.
  • More field lines per unit area perpendicular to the lines means a stronger field.

• Potential Energy Curves and Equipotentials

  • A potential energy curve plots potential energy as a function of position; equipotential lines trace lines of equal potential energy.
  • Equipotential lines trace lines of equal potential energy.
  • In , if you were to draw a straight horizontal line through the center, that would be an equipotential line.
  • Let us examine the physical explanation for the equipotentials lines in .
  • However, you do need to do work to move from one equipotential line to another.

• Constant Velocity Produces a Straight-Line

  • If a charged particle's velocity is parallel to the magnetic field, there is no net force and the particle moves in a straight line.
  • Because velocity is a vector, the direction remains unchanged along with the speed, so the particle continues in a single direction, such as with a straight line.
  • In this case a charged particle can continue with straight-line motion even in a strong magnetic field.
  • In the case above the magnetic force is zero because the velocity is parallel to the magnetic field lines.
  • Identify conditions required for the particle to move in a straight line in the magnetic field

• Helical Motion

  • shows how electrons not moving perpendicular to magnetic field lines follow the field lines.
  • The component of velocity parallel to the lines is unaffected, and so the charges spiral along the field lines.
  • Charged particles approaching magnetic field lines may get trapped in spiral orbits about the lines rather than crossing them, as seen above.
  • Those particles that approach middle latitudes must cross magnetic field lines, and many are prevented from penetrating the atmosphere.
  • This force slows the motion along the field line and here reverses it, forming a "magnetic mirror. "

• Instananeous Velocity: A Graphical Interpretation

  • Instantaneous velocity is the velocity of an object at a single point in time and space as calculated by the slope of the tangent line.
  • To do this, we find a line that represents our velocity in that moment, shown graphically in.
  • That line would be the line tangent to the curve at that point.
  • This would result in a curvy line when graphed with distance over time.
  • The velocity at any given moment is defined as the slope of the tangent line through the relevant point on the graph

• Electric vs. Magnetic Forces

  • The angle dependence of the magnetic field also causes charged particles to move perpendicular to the magnetic field lines in a circular or helical fashion, while a particle in an electric field will move in a straight line along an electric field line.
  • The electric field lines from a positive isolated charge are simply a sequence of evenly-spaced, radially directed lines pointed outwards from the charge.
  • The electric field is directed tangent to the field lines.
  • Of course, we imagine the field lines are more densely packed the larger the charges are.
  • Charged particles will spiral around these field lines, as long as the particles have some non-zero component of velocity directed perpendicular to the field lines .