Gioko, A. (2007). Eds AHL Topic 9.3 Electric Field, potential and Energy

Gioko, A. (2007). Eds Electric Potential Energy If you want to move a charge closer to a charged sphere you have to push against the repulsive force If you want to move a charge closer to a charged sphere you have to push against the repulsive force You do work and the charge gains electric potential energy. You do work and the charge gains electric potential energy. If you let go of the charge it will move away from the sphere, losing electric potential energy, but gaining kinetic energy. If you let go of the charge it will move away from the sphere, losing electric potential energy, but gaining kinetic energy.

Gioko, A. (2007). Eds When you move a charge in an electric field its potential energy changes. When you move a charge in an electric field its potential energy changes. This is like moving a mass in a gravitational field. This is like moving a mass in a gravitational field.

Gioko, A. (2007). Eds The electric potential V at any point in an electric field is the potential energy that each coulomb of positive charge would have if placed at that point in the field. The electric potential V at any point in an electric field is the potential energy that each coulomb of positive charge would have if placed at that point in the field. The unit for electric potential is the joule per coulomb (J C ‑ 1 ), or the volt (V). The unit for electric potential is the joule per coulomb (J C ‑ 1 ), or the volt (V). Like gravitational potential it is a scalar quantity. Like gravitational potential it is a scalar quantity.

Gioko, A. (2007). Eds In the next figure, a charge +q moves between points A and B through a distance x in a uniform electric field. In the next figure, a charge +q moves between points A and B through a distance x in a uniform electric field. The positive plate has a high potential and the negative plate a low potential. The positive plate has a high potential and the negative plate a low potential. Positive charges of their own accord, move from a place of high electric potential to a place of low electric potential. Positive charges of their own accord, move from a place of high electric potential to a place of low electric potential. Electrons move the other way, from low potential to high potential. Electrons move the other way, from low potential to high potential.

Gioko, A. (2007). Eds

In moving from point A to point B in the diagram, the positive charge +q is moving from a low electric potential to a high electric potential. In moving from point A to point B in the diagram, the positive charge +q is moving from a low electric potential to a high electric potential. The electric potential is therefore different at both points. The electric potential is therefore different at both points.

Gioko, A. (2007). Eds In order to move a charge from point A to point B, a force must be applied to the charge equal to qE In order to move a charge from point A to point B, a force must be applied to the charge equal to qE (F = qE). force is applied through a distance x, then work has to be done to move the charge, and there is an electric potential difference between the two points. force is applied through a distance x, then work has to be done to move the charge, and there is an electric potential difference between the two points. work done is equivalent to the energy gained or lost in moving the charge through the electric field. work done is equivalent to the energy gained or lost in moving the charge through the electric field.

Gioko, A. (2007). Eds If a charge moves at an angle θ to an electric field, the component of the displacement parallel to the electric field is used as shown in the next figure.

Gioko, A. (2007). Eds Electric Potential Difference Potential difference What is difference in potential between two points in an electric field The potential difference or p.d. is the energy transferred when one coulomb of charge passes from one point to the other point.

Gioko, A. (2007). Eds The diagram shows some values of the electric potential at points in the electric field of a positively ‑ charged sphere What is the p.d. between points A and B in the diagram?

Gioko, A. (2007). Eds Change in Energy Energy transferred, This could be equal to the amount of electric potential energy gained or to the amount of kinetic energy gained W = charge (q) x p.d.(V) W = charge (q) x p.d.(V) (joules) (coulombs) (volts) (joules) (coulombs) (volts)

Gioko, A. (2007). Eds The Electronvolt One electron volt (1 eV) is defined as the energy acquired by an electron as a result of moving through a potential difference of one volt. W = q x V charge on an electron or proton is 1.6 x C Then W = 1.6 x C x 1V W = 1.6 x J W = 1.6 x J Therefore 1 eV = 1.6 x J

Gioko, A. (2007). Eds Electric Potential due to a Point Charge The electric potential at a point in an electric field is defined as being numerically equal to the work done in bringing a unit positive charge from infinity to the point. Electric potential is a scalar quantity and it has the volt V as its unit. Based on this definition, the potential at infinity is zero.

Gioko, A. (2007). Eds Consider a point r metres from a charged object. The potential at this point can be calculated using the following Consider a point r metres from a charged object. The potential at this point can be calculated using the following

Gioko, A. (2007). Eds Electric Field Strength and Potential Suppose that the charge +q is moved a small distance by a force F from A to B so that the force can be considered constant. Suppose that the charge +q is moved a small distance by a force F from A to B so that the force can be considered constant. What is the work done?

Gioko, A. (2007). Eds The work done is given by: ΔW = Fx Δx The force F and the electric field E are oppositely directed, and we know that: F = ‑ q x E Therefore, the work done can be given as: ΔW = ‑ qE x Δ x = qV Therefore E = - ΔV / Δx This is the potential gradient.

Gioko, A. (2007). Eds Electric Field and Potential due to a charged sphere

Gioko, A. (2007). Eds In a charged sphere the charge distributes itself evenly over the surface. In a charged sphere the charge distributes itself evenly over the surface. Every part of the material of the conductor is at the same potential. Every part of the material of the conductor is at the same potential. Electric potential at a point is defined as Electric potential at a point is defined as being numerically equal to the work done in bringing a unit positive charge from infinity to that point, it has a constant value in every part of the material of the conductor potential is the same at all points on the conducting surface, then potential is the same at all points on the conducting surface, then Δ V / Δx is zero. But E = ‑ Δ V / Δ x. The electric field inside the conductor is zero. There is no electric field inside the conductor. The electric field inside the conductor is zero. There is no electric field inside the conductor.

Gioko, A. (2007). Eds

Equipotentials Regions in space where the electric potential of a charge distribution has a constant value are called equipotentials. Regions in space where the electric potential of a charge distribution has a constant value are called equipotentials. The places where the potential is constant in three dimensions are called equipotential surfaces, and where they are constant in two dimensions they are called equipotential lines. The places where the potential is constant in three dimensions are called equipotential surfaces, and where they are constant in two dimensions they are called equipotential lines.

Gioko, A. (2007). Eds They are in some ways analogous to the contour lines on topographic maps. Similar also to gravitational potential. In this case, the gravitational potential energy is constant as a mass moves around the contour lines because the mass remains at the same elevation above the earth's surface. The gravitational field strength acts in a direction perpendicular to a contour line.

Gioko, A. (2007). Eds Similarly, because the electric potential on an equipotential line has the same value, no work can be done by an electric force when a test charge moves on an equipotential. Therefore, the electric field cannot have a component along an equipotential, and thus it must be everywhere perpendicular to the equipotential surface or equipotential line. This fact makes it easy to plot equipotentials if the lines of force or lines of electric flux of an electric field are known.

Gioko, A. (2007). Eds For example, there are a series of equipotential lines between two parallel plate conductors that are perpendicular to the electric field. For example, there are a series of equipotential lines between two parallel plate conductors that are perpendicular to the electric field. There will be a series of concentric circles that map out the equipotentials around an isolated positive sphere. There will be a series of concentric circles that map out the equipotentials around an isolated positive sphere. The lines of force and some equipotential lines for an isolated positive sphere are shown in the next figures. The lines of force and some equipotential lines for an isolated positive sphere are shown in the next figures.

Gioko, A. (2007). Eds

Analogies exist between electric and gravitational fields. ( a) Inverse square law of force Coulomb's law is similar in form to Newton's law of universal gravitation. Coulomb's law is similar in form to Newton's law of universal gravitation. Both are inverse square laws with 1/(4πε) in the electric case corresponding to the gravitational constant G. Both are inverse square laws with 1/(4πε) in the electric case corresponding to the gravitational constant G. The main difference is that whilst electric forces can be attractive or repulsive, gravitational forces are always attractive. The main difference is that whilst electric forces can be attractive or repulsive, gravitational forces are always attractive. Two types of electric charge are known but there is only one type of gravitational mass. Two types of electric charge are known but there is only one type of gravitational mass. By comparison with electric forces, gravitational forces are extremely weak. By comparison with electric forces, gravitational forces are extremely weak.

Gioko, A. (2007). Eds

(b) Field strength (b) Field strength The field strength at a point in a gravitational field is defined as the force acting per unit mass placed at the point. The field strength at a point in a gravitational field is defined as the force acting per unit mass placed at the point. Thus if a mass m in kilograms experiences a force F in newtons at a certain point in the earth's field, the strength of the field at that point will be F/m in newtons per kilogram. Thus if a mass m in kilograms experiences a force F in newtons at a certain point in the earth's field, the strength of the field at that point will be F/m in newtons per kilogram. This is also the acceleration a the mass would have in metres per second squared if it fell freely under gravity at this point (since F = ma). This is also the acceleration a the mass would have in metres per second squared if it fell freely under gravity at this point (since F = ma). The gravitational field strength and the acceleration due to gravity at a point thus have the same value (i.e. F/m) and the same symbol, g, is used for both. At the earth's surface g = 9.8 N kg ‑ ' = 9.8 m s ‑ 2 (vertically downwards). The gravitational field strength and the acceleration due to gravity at a point thus have the same value (i.e. F/m) and the same symbol, g, is used for both. At the earth's surface g = 9.8 N kg ‑ ' = 9.8 m s ‑ 2 (vertically downwards).

Gioko, A. (2007). Eds

(c) Field lines and equipotentials These can also be drawn to represent gravitational fields but such fields are so weak, even near massive bodies, that there is no method of plotting field lines similar to those used for electric (and magnetic) fields. These can also be drawn to represent gravitational fields but such fields are so weak, even near massive bodies, that there is no method of plotting field lines similar to those used for electric (and magnetic) fields. Field lines for the earth are directed towards its centre and the field is spherically symmetrical. Field lines for the earth are directed towards its centre and the field is spherically symmetrical. Over a small part of the earth's surface the field can be considered uniform, the lines being vertical, parallel and evenly spaced. Over a small part of the earth's surface the field can be considered uniform, the lines being vertical, parallel and evenly spaced.

Gioko, A. (2007). Eds (d) Potential and p.d. Electric potentials and pds are measured in joules per coulomb (J C ‑ 1 ) or volts; Electric potentials and pds are measured in joules per coulomb (J C ‑ 1 ) or volts; gravitational potentials and pds are measured in joules per kilogram (J kg ‑ 1 ). gravitational potentials and pds are measured in joules per kilogram (J kg ‑ 1 ). As a mass moves away from the earth the potential energy of the earth ‑ mass system increases, transfer of energy from some other source being necessary. As a mass moves away from the earth the potential energy of the earth ‑ mass system increases, transfer of energy from some other source being necessary.

Gioko, A. (2007). Eds If infinity is taken as the zero of gravitational potential (i.e. a point well out in space where no more energy is needed for the mass to move further away from the earth) If infinity is taken as the zero of gravitational potential (i.e. a point well out in space where no more energy is needed for the mass to move further away from the earth) then the potential energy of the system will have a negative value except when the mass is at infinity. then the potential energy of the system will have a negative value except when the mass is at infinity. At every point in the earth's field the potential is therefore negative (see expression below), a fact which is characteristic of fields that exert attractive forces. At every point in the earth's field the potential is therefore negative (see expression below), a fact which is characteristic of fields that exert attractive forces.

Gioko, A. (2007). Eds

0bjectives covered Define electric potential and electric potential energy State and apply the expression for electric potential due to a point charge State and apply the formula relating electric field strength to electric potential gradient Determine the potential due to one or more point charges Describe and sketch the pattern of equipotential surfaces due to one and two point charges State the relation between equipotential surfaces and electric field lines Solve problems involving electric potential energy and electric potential.

Gioko, A. (2007). Eds NEXT UNIT IS ATOMIC PHYSICS CORE