Physics 30 Electrostatics Lesson 2 Coulomb's Law PDF

Physics 30 – Electrostatics – Lesson 2: Coulomb’s Law Historical Development ​ 1775, Franklin noted that a small neutral cork hanging near surface of an electrically charged metal can was strongly attracted to outside surface of can o​ When the same neutral cork was lowered insi...

Physics 30 – Electrostatics – Lesson 2: Coulomb’s Law Historical Development ​ 1775, Franklin noted that a small neutral cork hanging near surface of an electrically charged metal can was strongly attracted to outside surface of can o​ When the same neutral cork was lowered inside the can, it was not attracted to surface of can ▪​ appeared to be no net forces inside the can o​ Priestly, a house guest of Franklin at the time, reasoned that the appearance of no net electrical forces inside the metal can might be very similar to gravity within a hollow planet. ​ Shielding (Faraday’s Cage) o​ Charges align themselves around the surface to balance repulsive forces o​ Anywhere within the interior of a hollow conducting object, the vector sum of all the individual electric forces is zero Hollow Conducting Object o​ excess charges move to achieve static equilibrium, and they move as far apart as possible because of electrostatic forces of repulsion o​ In a hollow conducting object, all excess charges are still repelled outward. ▪​ However, they distribute evenly only on the outer surface of the conducting object. o​ There is no excess charge on the inner surface of the hollow object, no matter what the shape of the object is. o​ Most surprisingly, the electric field is zero everywhere inside the conductor, so there are no electric field lines anywhere inside a hollow conductor ▪​ Anywhere within the interior of a hollow conducting object, the vector sum of all the individual electric fields is zero. ​ For this reason, David Blaine inside the Faraday cage is not affected by the tremendous charges on the outside surface of the cage. Historical Development (continued) ​ Charles Coulomb (1738-1806) tested the relationship between electrostatic and gravitational forces using a torsion balance which was similar to a device that Cavendish had used to measure G. Coulomb’s Law ​ Coulomb found that the electrostatic force is…Directly proportional to the charges  ​ Inversely proportional to the square of the distance between them Coulomb’s Law Things to Consider… ​ Fe are very strong in comparison to Fg o​ Fe can be attractive or repulsive unlike Fg which is always attractive ​ When calculating Fe, do not include positive or negative signs for q o​ Assign a direction based on attraction or repulsion and use vector addition to find the resultant Example 1: Two equally charged particles have an attractive force of 3.56 × 104 N when they are separated by a distance of 0.34 cm. What is the charge on each particle? Example 2: Determine the net electrostatic force on C. Example 3: Three charges are lined up on the same plane. Charge A (+25 μC) is set 12.0 m away from Charge B (+78.0 μC). If an unknown Charge C is set between them, where will it come to rest in reference to Charge B? Physics 30 – Electrostatics – Lesson 4: Electric Fields Field ​ Michael Faraday (1791-1867) is credited with the modern “field” concept which solved the dilemma of “action at a distance.” ​ Field: a region of influence or interaction surrounding an object that causes another object to experience a force. Fields ​ Gravitational Field: The space surrounding a mass in which other masses will experience a force of attraction toward that mass. ​ Electric Field: The space surrounding a charge in which other charges will experience an electrostatic force of attraction/repulsion. Electric Fields ​ Electric Fields have the following characteristics: o​ They can be produced by either positive or negative charges. o​ They decrease in strength with increased distance. o​ They are vector fields like gravitational fields. Fields ​ Fields can be scalar or vector o​ E.g. of scalar field: temperature  ▪​ The direction of a gravitational field is shown by the direction of gravitational force on a small test mass placed in the field. ▪​ The direction of an electric field is the direction of the electric force on a small imaginary positive test charge placed in that field. Picturing the Electric Field Electric Fields surrounding source charges: ​ The strength of the electric field is indicated by the spacing between field lines. The field is stronger where the lines are closer together (densest). Electric Fields Lines Around Like Charges: Picturing the Electric Field (continued) Electric Fields Lines Around Unlike Charges: ​ 𝐸𝑛𝑒𝑡⃑ from two charges is a combination of the fields from each of the charges. The electric force at any point is tangent to the field line at that point. Electric Fields Lines around Oppositely Charged Parallel Plates: ​ The uniform spacing of electric field lines indicates that the electric field is of same magnitude everywhere except at the edges. Electric Fields within Conductors:  ​ There is no electric field inside the hollow conductor. o​ This is how shielding devices work. Electric fields cause forces to act on charged particles like those that run through computers and other electronics. In order to insulate theses devices from unwanted outside electric fields, they are housed in hollow conductors. Electric Field Strength ​ When another charge (qt) is placed within an existing electric field it experiences a force Electric Field Strength (Intensity) ​ Use for a radial field surrounding a source charge Example 1: The drawing below shows two charged objects A and B. Charge A produces an electric field at point P of 3.00 N/C [right] and charge B produces an electric field at point P of 2.00 N/C [down]. What is the net field at P? Example 2: 2.4 x 1020 excess e- are loaded onto a sphere with a diameter of 4.0 cm. What is the electric field intensity at a distance of 16 cm from the surface of the sphere? (Hint: What “r” distance is used for Coulomb's law?) What force would act on a +3.0 µC test charge at this point? Example 3: A 60 µC charge is placed in an electric field. If the mass of the charge is 0.25 mg, and it experiences an acceleration of 1.25x104 m/s2, what is the electric field strength at that point? Physics 30 – Electrostatics – Lesson 6: Electric Potential Comparing Gravitational and Electrical Differences Electrical Potential Formula: Gravitational Potential Energy ​ GPE is… o​ Lost as you move towards B o​ Gained as you move towards A o​ Unchanged if you move towards C ▪​ The work you do against the field is converted to GPE Electrical Potential Energy ​ If q+ is moved… o​ Toward A: EPE increases o​ Toward B: EPE decreases o​ Toward C: moving perpendicular to field so no work is done EPE does not change ▪​ Electric Potential Energy, Ep, is the energy of a charged object due to its position in an electric field. Gravitational Potential Difference ​ The change in gravitational potential energy per unit mass. o​ ∆Ep=mg∆h ∆𝐸𝑝 ▪​ 𝑚 =g∆h ∆𝐸𝑝 o​ Gravitational potential difference= 𝑚 =g∆h Electrical Potential Difference (∆V) ​ The change in electric potential energy per unit charge o​ It is the work done against electric forces to move a charge from one position to another in an electric field. o​ How much work is needed per Coulomb of charge something with more charge needs more work to move it Example 1: An alpha particle is placed in an electric field with a potential difference of 100 V. If the alpha particle is released within the field, what is the maximum speed that it could attain? Electron Volts (eV) ​ The electron-volt is a unit of energy. ​ It is the energy that one electron would have after accelerating across a potential difference of one volt. ▪​ E=qV ​ 1eV=1.60x10-19C ( )=1.60x10 1𝐽 𝐶 -19 J ​ 1eV = 1.60 × 10-19 J o​ Note: eV is not a metric unit so it cannot be used in any formulas! Parallel Plates ​ A simple way to create a potential difference → o​ The electric field lines are the same distance apart meaning 𝐸 is the same anywhere in the field o​ Thus its a uniform field o​ Will affect charged objects, but not neutral Equipotential Lines  ​ The equipotential lines, drawn parallel to the plates and perpendicular to electric field lines, represent a line of equal potential differences ​ it is only the difference in potential that matters o​ Move a proton from A B: ​ Work is done against the field so there is a gain potential energy o​ Move a proton from B A: ​ Work is done by the field so there is a loss in potential energy o​ Move a proton from A C: ​ Move perpendicular to field so no change in energy Physics 30 – Electrostatics – Lesson 7: Parallel Plates Parallel Plates ​ Connecting two parallel plates to a battery produces an electric field. o​ This field is uniform (𝐸⃑ is constant) except for at the ends. This means the electric field strength is the same everywhere inside the parallel plates. ▪​ This is called a parallel plate capacitor. ​ Recall: o​ Whenever work is done on a charge to move it against the electric force caused by an electric field, the charge gains electric potential energy ▪​ W=Fed=∆E ∆𝐸 ▪​ The energy required per unit charge is: V= 𝑞 𝐹𝑒𝑑 𝐹𝑒 → ▪​ V= 𝑞 and 𝑞 =𝐸 → ​ … So V=𝐸𝑑 …Or… o​ Units for electric field strength are either N/C or V/m o​ Can only use for electric fields that are uniform or between parallel plates (point charges and charged spheres do not provide uniform fields)  o​ The potential difference across two charged plates can be measured with a voltmeter. Example 1: Two parallel plates are 16.0 mm apart. a)​ If we want a uniform field of 800 N/C between these plates, what potential difference must be applied? b)​ How much work is needed to move an alpha particle from the negative plate to the positive plate? Example 2: Two horizontal metal plates are held 4.0 cm apart. The lower plate has a potential of 16 V and the upper plate has a potential of 48 V. a)​ What is the electric potential at 1.0 cm, 2.0 cm, and 3.0 cm above the lower plate? b)​ What is the electric field strength (intensity) at each of these points? c)​ Sketch the electric field between the plates. Different Types of Motion ​ When a charged particle’s initial motion is… o​ Parallel to Field: Fe is similar to the Fg on falling masses o​ Conservation of Energy CAN be applied ​ When a charged particle’s initial motion is… o​ Perpendicular to field: Fe is similar to Fg in that both forces act at angle to motion and hence, cause parabolic projectile motion ▪​ Two types of Motion (UAM and UM) so a kinematics (projectile motion) solution is easiest. Physics 30 – Electrostatics – Lesson 8: Millikan’s Experiment Particles in 𝐸⃑ and 𝑔⃑ ​ Recall that 𝐹𝑔⃑ is much smaller than 𝐹𝑒⃑ ​ Subatomic particles have a very small mass, so when they are in both electric and gravitational fields, 𝐹𝑒⃑ is the net force changing their motion o​ For “larger” masses (even mg or µg) 𝐹𝑔⃑ is a factor that needs to be considered ▪​ Consider a negatively charged “larger” mass in a uniform electric field ​ If it is accelerating: ​ If it is suspended: Example 1: An unknown charge is placed onto a 0.050 mg particle which is placed between two horizontal plates. The plates are 8.0 mm apart with a potential difference of 5 000 V across them. If the particle is suspended between the plates, what is the charge on the particle? How many excess electrons are on the particle? Example 2: A particle with a charge of +2.10 µC moves with a horizontal velocity of 4.00 m/s between two parallel plates, as shown below. The mass of the particle is 1.05 x 10-2 g. The electric field between the plates has a magnitude of 25.0 N/C. The particle also experiences the effects of the gravitational field. What is the velocity of the particle the instant it strikes a plate? What plate does the particle strike? Millikan’s Experiment ​ In 1897, JJ Thomson measured the charge to mass ratio of the electron ​ Between 1906-1913, Millikan conducted the “Oil Drop Experiment” to find the charge on an electron ​ Millikan placed charged oil droplets in a parallel plate capacitor and adjusted the potential difference so that the electric field exerted an upward force that balanced the downward gravitational force.  ​ Using a small microscope, Millikan observed the motion of the droplets and measured their size ​ From droplet’s radius and density of the oil he could determine its mass Millikan’s Assumptions ​ All e- are identical each has same amount of charge ​ Mass of an e- is so small that +/- a few will not significantly change mass of an oil droplet ​ Amount of charge on the oil droplet will be a whole number multiple of the charge of one e- Millikan’s Findings ​ Millikan found charges that were all whole number multiples of -1.6 × 10-19 C. ​ He concluded that charge is quantized. ​ The smallest or elementary charge is 1.6024 x 10-19 C, the charge of 1 e-