Examples of perpendicular lines in the following topics:
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- Two lines are perpendicular to each other if they form congruent adjacent angles.
- This means that if the slope of one line is $m$, then the slope of its perpendicular line is $\frac{-1}{m}$.
- Therefore, the equation of the line perpendicular to the given line has a slope of $-4$ and a $y$-intercept of $12$.
- The line $f(x)=3x-2$ in red is perpendicular to line $g(x)=\frac{-1}{3}x+1$ in blue.
- Write equations for lines that are parallel and lines that are perpendicular
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- A line graph is a type of chart which displays information as a series of data points connected by straight line segments.
- A line graph is a type of chart which displays information as a series of data points connected by straight line segments.
- A line chart is often used to visualize a trend in data over intervals of time – a time series – thus the line is often drawn chronologically.
- A line chart is typically drawn bordered by two perpendicular lines, called axes.
- If lines are drawn parallel to both axes, the resulting lattice is called a grid.
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- At large distances from the center, the hyperbola approaches two lines, its asymptotes, which intersect at the hyperbola's center.
- The distance b (not shown in below) is the length of the perpendicular segment from either vertex to the asymptotes.
- The two focal points are labeled F1 and F2, and the thin black line joining them is the transverse axis.
- The perpendicular thin black line through the center is the conjugate axis.
- The two thick black lines parallel to the conjugate axis (thus, perpendicular to the transverse axis) are the two directrices, D1 and D2.
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- Helical motion results when the velocity vector is not perpendicular to the magnetic field vector.
- What if the velocity is not perpendicular to the magnetic field?
- 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.
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- 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.
- Recall that work is zero if force is perpendicular to motion; in the figures shown above, the forces resulting from the electric field are in the same direction as the electric field itself.
- So we note that each of the equipotential lines must be perpendicular to the electric field at every point.
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- 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 is directed tangent to the field lines.
- 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 .
- A magnetic field may also be generated by a current with the field lines envisioned as concentric circles around the current-carrying wire.The magnetic force at any point in this case can be determined with the right hand rule, and will be perpendicular to both the current and the magnetic field.
- The direction of the magnetic force on a moving charge is perpendicular to the plane formed by v and B and follows right hand rule–1 (RHR-1) as shown.
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- 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.
- It is exactly proportional to the number of lines per unit area perpendicular to the lines (called the areal density).
- (C) When the wire is in the plane of the paper, the field is perpendicular to the paper.
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- 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.
- Since they are located radially around a charged body, they are perpendicular to electric field lines, which extend radially from the center of a charged body.
- 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.
- Describe the shape of the equipotential lines for several charge configurations
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- Electric flux is proportional to the number of electric field lines going through a virtual surface.
- If the electric field is uniform, the electric flux passing through a surface of vector area S is $\Phi_E = \mathbf{E} \cdot \mathbf{S} = ES \cos \theta$ where E is the magnitude of the electric field (having units of V/m), S is the area of the surface, and θ is the angle between the electric field lines and the normal (perpendicular) to S.
- For a non-uniform electric field, the electric flux dΦE through a small surface area dS is given by $d\Phi_E = \mathbf{E} \cdot d\mathbf{S}$ (the electric field, E, multiplied by the component of area perpendicular to the field).
- The red arrows for the electric field lines.
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- The direction of the magnetic force F is perpendicular to the plane formed by v and B, as determined by the right hand rule, which is illustrated in the figure above.
- The right hand rule states that: to determine the direction of the magnetic force on a positive moving charge, ƒ, point the thumb of the right hand in the direction of v, the fingers in the direction of B, and a perpendicular to the palm points in the direction of F.
- There are many field lines, represented accordingly by the fingers.
- Because the force is always perpendicular to the velocity vector, a pure magnetic field will not accelerate a charged particle in a single direction, however will produce circular or helical motion (a concept explored in more detail in future sections).
- The direction of the magnetic force on a moving charge is perpendicular to the plane formed by v and B and follows right hand rule–1 (RHR-1) as shown.