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Summarize the Gauss's law results. Give answers in terms of relevant parameters such as lenc:: а. What is the electric field at a distance r from the center of a spherical charge distribution? b. What is the electric field at a distance r from the center of a cylindrical charge distribution? c. What is the electric field at a distance x from a large thin sheet with charge spreaded uniformly over its surface? d. What is the electric field inside a conductor in electrostatic equilibrium? е. What is the electric field just outside a conductor in electrostatic equilibrium?

Summarize the Gauss's law results. Give answers in terms of relevant parameters such as lenc:: а. What is the electric field at a distance r from the center of a spherical charge distribution? b. What is the electric field at a distance r from the center of a cylindrical charge distribution? c. What is the electric field at a distance x from a large thin sheet with charge spreaded uniformly over its surface? d. What is the electric field inside a conductor in electrostatic equilibrium? е. What is the electric field just outside a conductor in electrostatic equilibrium?

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3. Assume a solid conductor is placed next to a negatively charged sphere. This After this activity, you should know: The electric field inside and just outside a conductor in electrostatic equilibrium. causes the surface of the conductor near the sphere to become positively charged so that the net electric field inside the conductor is zero. 5. A neutral spherical conducting shell of radius 2R has a O How to find the charge on different surfaces of a conductor. concentric spherical hole of radius R inside it. There is a Now we cut a hole so that it is entirely encased by the conductor. point charge +2Q at the center of the hole. 1. What is true of a conductor in electrostatic equilibrium? Electrostatic equilibrium means that there is no current, i.e., no moving charges. More than one choice may be true. Circle all true statements. Does removing part of the inside of the conductor affect the electric field? What is the charge on the inner surface of the shell? a. а. xx X qinner = -2 No The electric field inside a conductor in equilibrium is zero. This is because any external electric field will cause the free charges in the conductor to redistribute to the surface until the electric field of these charges cancel out the external electric field leading to no net field inside the conductor. b. What is the electric field inside the hole? cross-section of 3D conductor The electric field is always zero inside a conductor even if there is a current going through the conductor. E = 0 inside hole b. What is the charge on the outer surface of the The electric field just outside the surface of the conductor is always perpendicular to the surface. shell? The electric field just outside the surface of the conductor is always parallel to the surface. c. Explain why sensitive equipment is often placed inside conductors. For example, circuit boards are typically -outer = +2 The electric field just outside the surface of the conductor is always zero. shipped in foil-lined bags while cell phone signals are weaker inside warehouses with metal sides. Any unbalanced charge must be on the surface of the conductor. They do this to block potentially harmful signals and electric fields from damaging or interfering with the cargo. 2. If you look very close to the surface on a conductor it will look flat. Just as the Earth appears flat to us c. Ma a graph of the elect field as a function of r, because we are on the surface. We want to find the the distance from the center of the shell. E R 2R 3R 4R 5R 4. Now we want to find the charge on the inner and outer surfaces of conductors. electric field at a point P just outside the conductor. Assume the conducting surface near P has a positive h' A solid conductor has a hole inside. Inside the hole there is a point charge of +3µC. r_{distance from center) +3uc charge per area n. We draw a Gaussian cylinder of radius R and height 2h cutting through the surface. The net charge of the conductor is -2 µC. That is, the sum of the charge on the inner and outer surfaces of the conductor is –2 µc. a. What is the flux through the curved portion of the a. What kind of charge (positive or negative) will be attracted to the inner surface 6. A capacitor is a device to store charge. The parallel plate capacitor Gaussian surface? Write the answer in terms of the Conductor of the conductor? consists of two large flat square conducting plates of sides L. One plate has charge +3Q and the other plate has opposite charge 3 – unknown electric field E, R and/or h. Negative L Q. Assume that the gap between the plates d is small compared to L. Ignore edge effects. DEds = DEAS cos 0 b. The dashed line represents a three-dimensional Gaussian surface which is entirely inside the conductor but J-ms]= outside the hole. What is the electric flux through this surface? A proton (mass M, charge +e) enters the region between the plates DEAS cos (90) = 0 = PE = 0 from the bottom as shown. Its initial velocity is v, straight upwards. -3Q b. What is the flux through the bottom endcap? Determine how far the proton moves horizontally as it goes through +3Q Based on your result for (b), what is the total charge enclosed by the Gaussian surface? gap between the plates. Assume the deflection is small enough it С. does not hit the plates. Gravitational forces are negligible. lenclosed = 0 L What is the flux through the top endcap? 3Q e L2 E0 c. eo F = EdS cos 0 = TER? d. Based on your result for (c), what must be the charge on the inner surface? Tinside + 3µC = 0 F 3Qe v0 a linside = -3µC megl? m d. Write the charge enclosed by the Gaussian surface in terms of 7, R and/or h? horizontal displacement (x) = a.t genc ηπR? 3Qe t e. Based on your result for (d) and the fact the total charge of the conductor is –2 µC, what is the charge on the е. Use Gauss's law to find the electric field just outside the conductor. outer surface of the conductor? L vertical displacement = v0t => t = vo ETR? qenc => E = Eo Inet = qinside + 9outside E0 -2µC = -3µC +qouter €0 louter = 1µC 3Qe => X = mɛgLvo
Transcribed Image Text:3. Assume a solid conductor is placed next to a negatively charged sphere. This After this activity, you should know: The electric field inside and just outside a conductor in electrostatic equilibrium. causes the surface of the conductor near the sphere to become positively charged so that the net electric field inside the conductor is zero. 5. A neutral spherical conducting shell of radius 2R has a O How to find the charge on different surfaces of a conductor. concentric spherical hole of radius R inside it. There is a Now we cut a hole so that it is entirely encased by the conductor. point charge +2Q at the center of the hole. 1. What is true of a conductor in electrostatic equilibrium? Electrostatic equilibrium means that there is no current, i.e., no moving charges. More than one choice may be true. Circle all true statements. Does removing part of the inside of the conductor affect the electric field? What is the charge on the inner surface of the shell? a. а. xx X qinner = -2 No The electric field inside a conductor in equilibrium is zero. This is because any external electric field will cause the free charges in the conductor to redistribute to the surface until the electric field of these charges cancel out the external electric field leading to no net field inside the conductor. b. What is the electric field inside the hole? cross-section of 3D conductor The electric field is always zero inside a conductor even if there is a current going through the conductor. E = 0 inside hole b. What is the charge on the outer surface of the The electric field just outside the surface of the conductor is always perpendicular to the surface. shell? The electric field just outside the surface of the conductor is always parallel to the surface. c. Explain why sensitive equipment is often placed inside conductors. For example, circuit boards are typically -outer = +2 The electric field just outside the surface of the conductor is always zero. shipped in foil-lined bags while cell phone signals are weaker inside warehouses with metal sides. Any unbalanced charge must be on the surface of the conductor. They do this to block potentially harmful signals and electric fields from damaging or interfering with the cargo. 2. If you look very close to the surface on a conductor it will look flat. Just as the Earth appears flat to us c. Ma a graph of the elect field as a function of r, because we are on the surface. We want to find the the distance from the center of the shell. E R 2R 3R 4R 5R 4. Now we want to find the charge on the inner and outer surfaces of conductors. electric field at a point P just outside the conductor. Assume the conducting surface near P has a positive h' A solid conductor has a hole inside. Inside the hole there is a point charge of +3µC. r_{distance from center) +3uc charge per area n. We draw a Gaussian cylinder of radius R and height 2h cutting through the surface. The net charge of the conductor is -2 µC. That is, the sum of the charge on the inner and outer surfaces of the conductor is –2 µc. a. What is the flux through the curved portion of the a. What kind of charge (positive or negative) will be attracted to the inner surface 6. A capacitor is a device to store charge. The parallel plate capacitor Gaussian surface? Write the answer in terms of the Conductor of the conductor? consists of two large flat square conducting plates of sides L. One plate has charge +3Q and the other plate has opposite charge 3 – unknown electric field E, R and/or h. Negative L Q. Assume that the gap between the plates d is small compared to L. Ignore edge effects. DEds = DEAS cos 0 b. The dashed line represents a three-dimensional Gaussian surface which is entirely inside the conductor but J-ms]= outside the hole. What is the electric flux through this surface? A proton (mass M, charge +e) enters the region between the plates DEAS cos (90) = 0 = PE = 0 from the bottom as shown. Its initial velocity is v, straight upwards. -3Q b. What is the flux through the bottom endcap? Determine how far the proton moves horizontally as it goes through +3Q Based on your result for (b), what is the total charge enclosed by the Gaussian surface? gap between the plates. Assume the deflection is small enough it С. does not hit the plates. Gravitational forces are negligible. lenclosed = 0 L What is the flux through the top endcap? 3Q e L2 E0 c. eo F = EdS cos 0 = TER? d. Based on your result for (c), what must be the charge on the inner surface? Tinside + 3µC = 0 F 3Qe v0 a linside = -3µC megl? m d. Write the charge enclosed by the Gaussian surface in terms of 7, R and/or h? horizontal displacement (x) = a.t genc ηπR? 3Qe t e. Based on your result for (d) and the fact the total charge of the conductor is –2 µC, what is the charge on the е. Use Gauss's law to find the electric field just outside the conductor. outer surface of the conductor? L vertical displacement = v0t => t = vo ETR? qenc => E = Eo Inet = qinside + 9outside E0 -2µC = -3µC +qouter €0 louter = 1µC 3Qe => X = mɛgLvo
7. Summarize the Gauss's law results. Give answers in terms of relevant parameters such as lenc.: а. What is the electric field at a distance r from the center of a spherical charge distribution? b. What is the electric field at a distance r from the center of a cylindrical charge distribution? C. What is the electric field at a distance x from a large thin sheet with charge spreaded uniformly over its surface? d. What is the electric field inside a conductor in electrostatic equilibrium? е. What is the electric field just outside a conductor in electrostatic equilibrium?
Transcribed Image Text:7. Summarize the Gauss's law results. Give answers in terms of relevant parameters such as lenc.: а. What is the electric field at a distance r from the center of a spherical charge distribution? b. What is the electric field at a distance r from the center of a cylindrical charge distribution? C. What is the electric field at a distance x from a large thin sheet with charge spreaded uniformly over its surface? d. What is the electric field inside a conductor in electrostatic equilibrium? е. What is the electric field just outside a conductor in electrostatic equilibrium?
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