#### Equipotential lines of a dipole

Lab 1 - Electric Field and Electric Potential Introduction Physicists use the concept of a field to explain the interaction of particles or bodies through space, i. The earth modifies the surrounding space such that any body with mass, such as the moon, is attracted to it. The gravitational field gets weaker as you go farther away from the source but never completely disappears. An electron modifies the space around it in such a way that other particles with like charge are repelled, while particles with the opposite charge are attracted. Like the gravitational field, the electric field gets weaker with distance from the source but is never completely gone.

Any charge placed in an electric field will experience a force, as will any mass placed in a gravitational field. Just as mass in a gravitational field has some potential energy, so does a charge in an electric field. In this lab, we will examine some aspects of electric field and electric potential. Discussion of Principles A charged body experiences a force F. Checkpoint 1: Ask your TA to check your field lines and calculations before proceeding. Checkpoint 2: Ask your TA to check your field lines and measurements before proceeding.

Checkpoint 3: Ask your TA to check your field lines and measurements before proceeding. Checkpoint 4: Ask your TA to check your field lines and measurements.Electrostatics and Electromagnetism. Electrostatics Charge, conductors, charge conservation Charges are either positive or negative. Zero charge is neutral. Like charges repel, unlike charges attract. Charge is quantized, and the unit of charge is the Coulomb.

Conductors are materials in which charges can move freely. Metals are good conductors. Charge is always conserved. You can't create or destroy charge, you can only transfer charge from one source to another. Insulators Insulators are materials in which charges can not move freely.

Nonmetals are good insulators. If the charges have opposite signs, the force is attractive. Electric field field lines Electric field is denoted by the vector E. Lines that are closer together denote stronger fields than lines that are farther apart. Electric fields come out of positive charges, and goes into negative charges.

Field lines for two negative charges are the same as those for two positive charges except that the direction of the field lines would be reversed. The direction and magitude of the field at any point in space can be calculated as the vector sum of all the field components there. Electric field in between a capacitor is uniform until it reaches the ends of the capacitor.

Electric field for wires runs radially perpendicular to the wire. Electric field for a cylinder runs radially perpendicular to the cylinder, and is zero inside the cylinder. Potential difference, absolute potential at point in space Absolute potential V is the amount of energy per charge that something possesses.

Traditionally, q 0 is the charge experiencing the potential. The magnitude of q 0 is very small. U is the electrical potential energy possessed by q 0. Equipotential lines Equipotential lines are places where the potential is the same. Equipotential lines are always perpendicular to electric field lines. Electrostatic induction Induction does not involve any type of conduction.

## Electrostatics and Electromagnetism

The classical example of electrostatic induction is picking up pieces of paper using a comb rubbed against fur. It's called electrostatic induction because it's static - the charged species polarizes non-charged species by simply being there. This is not the same as electromagnetic induction, which is how electric generators work. Luckily electromagnetic induction is not listed as an official AAMC topic. The net electric flux through any enclosed surface is totally dependent on the charge inside.

If there's no charge inside, then the net electric flux through the enclosure is zero. An important application of Gauss's law is the Faraday cage.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It only takes a minute to sign up.

Consider an electric dipole as in the figure. If I understand correctly, electric potential is the amount of work done per unit charge in bringing a charge from infinity to a distance r from a charge.

But consider moving along the equipotential line from infinity to a point along the equipotential line. Surely the work done to move the charge must be zero, since we are moving along an equipotential line. However, the electrostatic field is conservative, so work done in moving from infinity to a given point should be the same along any path.

Therefore, work done in moving a charge from infinity to a point close to a dipole is zero. Equipotential lines are always at right angles with the electric field most clearly shown in the centermost equipotential line. To move a charge along an equipotential line, you'd need to supply two forces: one to cancel out the net force from the two charges, and the other to move it along the equipotential. EDIT : So just to clarify, the electric field's contribution to the total work is zero, but the electric field on its own will never be able to pull the particle down from infinity.

Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Electric potential energy and equipotential lines Ask Question. Asked 2 years, 7 months ago. Active 2 years, 7 months ago. Viewed 2k times. This is clearly not the case, where have I gone wrong?? Thank you! This only applies in the case with where a single point charge causes the potential or other cases with the same symmetry. In other cases you should think about bringing a charge to a particular point in space.

Active Oldest Votes. So rather than saying the work done along an equipotential line is zero, I should rather say the work done by the electric field along an equipotential line is zero?

Yup you got it! I guess rectilinear equipotential lines can be followed with constant speed, without the need of tangential forces, actually requiring no work at all.Equipotential surfaces can be shown as lines in two dimensions to provide a quantitative way of viewing electric potential.

Every point on a given line is at the same potential. Equipotential surfaces are the orthogonal trajectories family of curves in the plane that intersect another family of curves at right angles of electric field lines.

Any electrostatic conservative field line penetrates such a surface normally perpendicularly. The electric field is always perpendicular to the equipotential surface which means that a charged particle moving along a equipotential surface always moves perpendicular to the electric force, therefore the electric force doesn't work on the particle moving along the equipotential surface. The value of electrostatic potential at any two or more given points on such a surface is the same and is a constant.

The work done by the field force in moving a charge along this surface is zero because there is no difference in potential between the initial and final points. Equipotential surfaces have to do with the change in electric potential. That is, as you go from one equipotential surface to another, the electric potential changes. When a charge moves from one equipotential surface to another either its kinetic energy increases if the change is from a higher to a lower potential or work must be done on it if the change is from a lower to a higher potential.

The electric force, like the gravitational force, is conservative. That is, if you do work on a charge to move it to a higher electric potential, this work can in principle be recovered in the form of kinetic energy as the charge "falls" back through this change in potential. Equipotential surfaces due to a dipole. Equipotential lines of two different positive charges and negative charges.

Properties of Equipotential Surfaces : Work done in moving a test charge over an equipotential surface is zero.

Electric field is normal to the equipotential surface. These surfaces helps in distinguishing region of strong field from that of weak field.

Equipotential surfaces gives the direction of electric field. These surfaces never cross each other.Equipotential lines are like contour lines on a map which trace lines of equal altitude. In this case the "altitude" is electric potential or voltage. Equipotential lines are always perpendicular to the electric field. In three dimensions, the lines form equipotential surfaces.

Movement along an equipotential surface requires no work because such movement is always perpendicular to the electric field. The electric potential of a point charge is given by. The equipotential lines are therefore circles and a sphere centered on the charge is an equipotential surface. The dashed lines illustrate the scaling of voltage at equal increments - the equipotential lines get further apart with increasing r.

The electric potential of a dipole show mirror symmetry about the center point of the dipole. They are everywhere perpendicular to the electric field lines.

The plane perpendicular to the line between the charges at the midpoint is an equipotential plane with potential zero. Equipotential Lines Equipotential lines are like contour lines on a map which trace lines of equal altitude. Index Voltage concepts. Equipotential Lines: Constant Field. For parallel conducting plates like those in a capacitorthe electric field lines are perpendicular to the plates and the equipotential lines are parallel to the plates.

Equipotential lines: point charge The electric potential of a point charge is given by so that the radius r determines the potential.

### Equipotential Lines

Equipotential lines: dipole The electric potential of a dipole show mirror symmetry about the center point of the dipole. Index Voltage concepts Electric dipole concepts.Compare conductivity and resistivity of an ideal conductor, commenting on the presence of ideal conductors in nature. An ideal conductor is one that exists only in the world of theory. This means that, ideally, it needs a minute amount of voltage potential difference to carry an extremely high amperage current. The principle of near-zero resistance is akin to that of frictionless surfaces: tTheoretically, with the slightest force voltagean object current on a frictionless surface zero-resistance conductor can proceed without restriction.

The electric field E tan and electric flux density D tan tangential to the surface of a conductor must be equal to 0. This is because any such field or flux that is tangential to the surface of the conductor must also exist inside the conductor, which by definition touches the tangential field or density at one point. If an electric field exists inside the metal, there must be a drop in voltage between any two points along the surface of the metal.

In a perfect conductor this drop should not exist because it implies a less-than-infinite conductivity. This means that the electric field inside a perfect conductor is 0. The charges along the surface all act equally and opposite to one another, and their sum at any point is equal to 0. Charge distribution may vary depending on shape, but the potential over the surface of an ideal conductor is, at electrostatic equilibrium, constant throughout.

Charge Distribution on a Conductor with an Irregular Surface : Curvature causes electric field lines to extend such that they further distance themselves from one another with increasing distance from the conductor surface. As such, charges and field lines aggregate around areas of curvature.

Electric potentials are commonly found in the body, across cell membranes and in the firing of neurons. Electric potentials are not limited in function to inorganic processes. In fact, they can be commonly seen in living organisms. In humans, they are seen in cell membranes and nerve impulses in particular. Cell membranes are only semipermeable; water can freely travel in and out, but ions can be selectively admitted passage across them.

As a result, a cell can contain a concentration of a given ion that differs from that which exists outside. Thus, a potential, called the resting potential, is created on either side of the membrane. Resting membrane potential is approximately mV in skeletal muscle cells, mV in smooth muscle cells, to mV in astroglia, and to mV in neurons. Potentials can change as ions move across the cell membrane. This can occur passively, as ions diffuse through ion channels in the membrane.

No energy is required for this to occur, and therefore ions can only move from areas of higher concentration to those of lower concentration. Active transport of ions across a cell membrane is also a possibility. This involves ion pumps using energy to push an ion from an area of lower concentration to one of higher concentration. When the brain decides on an action, it sends an impulse that cascades to the extremity where a muscle contracts.

Neurons receive an impulse at the dendrites. This impulse is passed through the axon, a long extension of the cell, in the form of an electrical potential created by differing concentrations of sodium and potassium ions on either side of a membrane in the axon.

The Neuron : Neurons receive an impulse at the dendrites. When the signal reaches the end of the axon, neurotransmitters are released, which then are received by the dendrites of the next neuron. The next neuron repeats the process outlined above. Equipotential lines depict one-dimensional regions in which the electric potential created by one or more nearby charges is constant.

Equipotential lines depict one-dimensional regions in which the electric potential created by one or more nearby charges has a constant value.

## Lab 1 - Electric Field and Electric Potential

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.We can represent electric potentials voltages pictorially, just as we drew pictures to illustrate electric fields. Of course, the two are related. Consider Figure 1, which shows an isolated positive point charge and its electric field lines. Electric field lines radiate out from a positive charge and terminate on negative charges.

While we use blue arrows to represent the magnitude and direction of the electric field, we use green lines to represent places where the electric potential is constant. These are called equipotential lines in two dimensions, or equipotential surfaces in three dimensions. The term equipotential is also used as a noun, referring to an equipotential line or surface. The potential for a point charge is the same anywhere on an imaginary sphere of radius r surrounding the charge.

An equipotential sphere is a circle in the two-dimensional view of Figure 1. Since the electric field lines point radially away from the charge, they are perpendicular to the equipotential lines. Figure 1. An isolated point charge Q with its electric field lines in blue and equipotential lines in green. The potential is the same along each equipotential line, meaning that no work is required to move a charge anywhere along one of those lines. Work is needed to move a charge from one equipotential line to another.

Equipotential lines are perpendicular to electric field lines in every case. It is important to note that equipotential lines are always perpendicular to electric field lines.

Thus the work is. Work is zero if force is perpendicular to motion. Force is in the same direction as E, so that motion along an equipotential must be perpendicular to E. More precisely, work is related to the electric field by. Note that in the above equation, E and F symbolize the magnitudes of the electric field strength and force, respectively. In other words, motion along an equipotential is perpendicular to E.

One of the rules for static electric fields and conductors is that the electric field must be perpendicular to the surface of any conductor. This implies that a conductor is an equipotential surface in static situations. There can be no voltage difference across the surface of a conductor, or charges will flow. One of the uses of this fact is that a conductor can be fixed at zero volts by connecting it to the earth with a good conductor—a process called grounding.

Grounding can be a useful safety tool. For example, grounding the metal case of an electrical appliance ensures that it is at zero volts relative to the earth. A conductor can be fixed at zero volts by connecting it to the earth with a good conductor—a process called grounding.

Because a conductor is an equipotential, it can replace any equipotential surface. Given the electric field lines, the equipotential lines can be drawn simply by making them perpendicular to the electric field lines.