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Essential idea: Electric charges and masses each influence the space around them and that influence can be represented through the concept of fields.
Nature of science:
Paradigm shift: The move from direct, observable actions being responsible for influence on an object to acceptance of a field’s “action at a distance” required a paradigm shift in the world of science. (2.3)
Understandings:
Gravitational fields
Electrostatic fields
Electric potential and gravitational potential
Field lines
Equipotential surfaces
Applications and skills:
Representing sources of mass and charge, lines of electric and gravitational force, and field patterns using an appropriate symbolism
Mapping fields using potential
Describing the connection between equipotential surfaces and field lines
Guidance:
Electrostatic fields are restricted to the radial fields around point or spherical charges, the field between two point charges and the uniform fields between charged parallel plates
Gravitational fields are restricted to the radial fields around point or spherical masses and the (assumed) uniform field close to the surface of massive celestial bodies and planetary bodies
Students should recognize that no work is done in moving charge or mass on an equipotential surface
Data booklet reference:
Theory of knowledge:
Although gravitational and electrostatic forces decrease with the square of distance and will only become zero at infinite separation, from a practical standpoint they become negligible at much smaller distances. How do scientists decide when an effect is so small that it can be ignored?
Utilization:
Knowledge of vector analysis is useful for this sub-topic (see Physics sub-topic 1.3)
Aims:
Aim 9: models developed for electric and gravitational fields using lines of forces allow predictions to be made but have limitations in terms of the finite width of a line
Central Body - Fields / Field Lines
Central Body - Fields / Field Lines
Gravitational Fields
Gravitational Fields
A gravitational field is a space where a small test mass experiences a force due to another mass.
Length of arrow proportional to (represent) slope of space-time curvature.
Gravitational Field Strength
Gravitational Field Strength
Show that the following equations are equivalent:
The gravitational field strength at a point is the force per unit mass experienced by a test mass at that point.
g = gravitational field strength (Effect)
F = Force Gravity (Cause)
m = mass of test object (not the central body) (Limiter)
Gravitational field strength at the surface of a planet
The gravitational field strength at the surface of a planet can be calculated by using the equation for gravitational field strength and substituting M and r by the mass and the radius of the planet respectively.
If we calculate the gravitational field strength at the surface of the Each using the mass and the radius of the Earth, we would obtain the value 9.81m/s^2, which is equal to the acceleration due to gravity on the surface of the Earth.
Different planets have different radii and masses. Consequently, different planets have different gravitational field strengths.
Central Body - Potentials
Central Body - Potentials
Gravitational Potential
Gravitational Potential
The gravitational potential ( V ) due to an object (central body) with mass M is given by the equation above.
The gravitational potential at infinity is zero.
Gravitational potential is always negative.
To calculate the gravitational potential due to multiple masses, simply add up the gravitational potential due to the individual masses.
NOTICE: Gravitational Potential depends ONLY on the mass of the central body and inversely related to the distance from the center of the central body.
DO: Using Potentials equation and the information below, show that Potentials describe the Energy per Mass at a specific point.
The gravitational potential (J/kg) at a point P is equal to work (J) done per unit mass (kg) required to take a test mass from infinity to point P.
Show that the following are equivalent:
Field Lines and Equipotential Surfaces
Field Lines and Equipotential Surfaces
Gravitational
Gravitational
Points with the same gravitational potential can be joined together to form an equipotential surface
Field lines are normal (perpendicular) to the equipotential surfaces.
The density of field lines is proportional to the field strength.
Far from the central body, the field line separation changes as the gravitational field strength changes. However, near the surface of the earth, the value of the gravitational field strength is relatively constant with radius as long as the change of radius is not too great.
Standing on Bleachers
Standing on Bleachers
Comparing field lines (path of least resistance), potentials (J/kg), and total energy (J).
Gravity Wells
Gravity Wells
Sample Questions / Problems
Sample Questions / Problems
1. P and S are two points on a gravitational equipotential surface around a planet. Q and R are two points on a different gravitational equipotential surface at a greater distance from the planet.
The greatest work done by the gravitational force is when moving a mass from
A. P to S
B. Q to R
C. R to P ✓
D. S to R
2. The diagram shows 5 gravitational equipotential lines. The gravitational potential on each line is indicated. A point mass m is placed on the middle line and is then released. Values given in MJ kg–1.
Which is correct about the direction of motion and the acceleration of the point mass? D
3, A moon of mass M orbits a planet of mass 100M. The radius of the planet is R and the distance between the centres of the planet and moon is 22R.
What is the distance from the centre of the planet at which the total gravitational potential has a maximum value?
A. 2R
B. 11R
C. 20R ✓
D. 2R and 20R
4. A satellite is in an orbit around the Earth. It is moved to a new orbit that is closer to the surface of the Earth. Which of the following correctly describes the changes in the gravitational potential energy and in the orbital speed of the satellite?
Essential Vocabulary
Essential Vocabulary
Equipotential for gravitational fields, an equipotential connects points of equal gravitational potential. When a charge or object moves from one point to another along an equipotential, no work is done. The angle between equipotentials and field lines is always 90°.
Field lines help us to visualize the shapes of electric and gravitational fields. Field lines leave the surface of an object at 90° to the surface, and are always at 90° to equipotential surfaces.
Gravitational field there is said to be a gravitational field when a gravitational force exists between two objects that both have mass. Gravitational fields are always attractive, and are directed downwards at 90° normal to the surface when close to the surface of an object.
Gravitational field strength (g) the ratio of the change in gravitational potential ΔVg (J kg–1) to the change in distance Δr (m), g =Vgr. , with the units N kg–1.
Gravitational potential (Vg) the gravitational potential Vg (J kg–1) at a distance r (m) from a single point mass M (kg) is given by Vg=-GMr, where G is the universal gravitational constant. The gravitational potential difference ΔVg at a point is the work done W (J) per unit mass in moving a test mass m (kg) from infinity to that point, V=Wm. Gravitational potential is defined to be zero at infinity.
Inverse-square law both the electrostatic force (FE=kq1q2r2) and the gravitational force (Fg=Gm1m2r2)obey the inverse-square law, that is, the force between two point charges of charge q1 and q2 , or two objects of mass m1 and m2, is inversely proportional to the square of the distance r between them.
Potential energy (EP) for a gravitational field the potential energy of a mass m (kg) at a point r (m) from another mass M (kg) is given by Ep(J)=mVg=-GMmr, where Vg (J kg–1) is the gravitational potential and G is the universal gravitational constant.
Circular Motion Problem - We will return to this later. (10 Nov 2022)
5. A planet is in a circular orbit around a star. The speed of the planet is constant. The following data are given:
Mass of planet = 8.0×10ˆ24 kg
Mass of star = 3.2×10ˆ30 kg
Distance from the star to the planet R = 4.4×10ˆ10 m.
A spacecraft is to be launched from the surface of the planet to escape from the star system. The radius of the planet is 9.1 × 103 km.
Explain why a centripetal force is needed for the planet to be in a circular orbit. [2]Calculate the value of the centripetal force. [1]Show that the gravitational potential due to the planet and the star at the surface of the planet is about −5 × 109J kg−1. [3]
Electric Fields and Potentials
Electric Fields and Potentials
Electric
Electric
Topic 5.1 is an in depth discussion of electric fields
Electric Potential
Electric Potential
The electric potential is given by
The electric potential difference is also known as voltage
Electric Fields
Electric Fields
An electrostatic field is a space where a small positive test charge experiences a force per unit charge.
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