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S22-1 An imaginary, spherical surface has radius 5.0m and is centered on the origin. A +15.0nC...
a) Consider a point charge q at the center of an imaginary box with side lengths...
a) Consider a point charge q at the center of an imaginary box with side lengths 2a. Explicitly calculate the flux of the electric field through the box and show that it agrees with Gauss's law. b) Suppose the electric field of a point charge q is proportional to 1/r3 instead of 1/r2. Does Gauss's law hold in this case? Hint: compute the electric flux through a sphere centered at the location of q. Is your answer dependent on your...
3. a) Consider a point charge q at the center of an imaginary box with side...
3. a) Consider a point charge q at the center of an imaginary box with side lengths 2a. Explicitly calculate the flux of the electric field through the box and show that it agrees with Gauss's law b) Suppose the electric field of a point charge q is proportional to 1/r3 instead of 1/r2. Does Gauss's law hold in this case? Hint: compute the electric fluz through a sphere centered at the location of q. Is your answer dependent on...
3. a) Consider a point charge q at the center of an imaginary box with side...
3. a) Consider a point charge q at the center of an imaginary box with side lengths 2a. Explicitly calculate the flux of the electric field through the box and show that it agrees with Gauss's law. b) Suppose the electric field of a point charge q is proportional to 1/r3 instead of 1/2. Does Gauss's law hold in this case? Hint: compute the electric flur through a sphere centered at the location of q. Is your answer dependent on...
Summary 583 Bridging Problem An imaginary sphere of radius R is centered at the origin, as...
Summary 583 Bridging Problem An imaginary sphere of radius R is centered at the origin, as shown in Pigure 17,37. A charge q is rigidly fixed to the x axis at +R/2 and a second charge g is at-R2. Finally, a proton (of mass and charge te) is released from rest oa the y axis. in terms of e, m, R of the proton at the moment it is released from y +R/4. (b) What are the magnitude and direction...
3). A thin spherical shell is centered at the origin with radius 1.8 meter. The shell...
3). A thin spherical shell is centered at the origin with radius 1.8 meter. The shell has a surface charge density of -5 C/m². At the center of the spherical shell (at the origin) there is a +2 C point charge. Calculate the magnitude of the electric field at 1.2 meters from the center of the spherical shell.
4. A spherically sym metric charge distribution has the following radial dependence for the volume charge...
4. A spherically sym metric charge distribution has the following radial dependence for the volume charge density ρ 0 if r > R where γ is a constant a) What units must the constant y have? b) Find the total charge contained in the sphere of radius R centered at the origin. c) Use the integral form of Gauss's law to determine the electric field in the region r < R. (Hint: if the charge distribution is spherically symmetric, what...
Only part f) please! 4 A spherically symmetric charge distribution has the following radial dependence for...
Only part f) please!
4 A spherically symmetric charge distribution has the following radial dependence for the volume charge density ρ ρ(r) If r > R where y is a constant a) What units must the constant y have? b) Find the total charge contained in the sphere of radius R centered at the origin c) Use the integral form of Gauss's law to determine the electric field in the region r < R. Hint: if the charge distribution is...
A sphere of radius R is centered at the origin. A constant magnetic field of magnitude...
A sphere of radius R is centered at the origin. A constant magnetic field of magnitude B is in the +k direction. What is the value of the magnetic flux that passes through the hemispherical surface that has z<0? (This is the half of the surface of the sphere in the region z<0.) Define the flux to be positive if it points from the inside of the sphere to the outside. a) 2 B b) -2B c) - TPB d)...
8) A Gaussian spherical surface of radius 0.20 m completely surrounds a collection of charges. A...
8) A Gaussian spherical surface of radius 0.20 m completely surrounds a collection of charges. A uniform electric field emerging from the charges has a value of.51 NC. a) Find the electric flux through the surface if the collection consists of a single charge. Use the Gauss Law to determine the magnitude of this charge inside the sphere. b)
A hollow sphere of radius a has uniform surface charge density σ and is centered at...
A hollow sphere of radius a has uniform
surface charge density σ and is centered at the origin. It
sits inside a bigger sphere, also centered at the origin, with
radius b > a and uniform
surface charge density −σ. Because of the spherical
symmetry, the electric field will have the form () =
E(r) r̂, where
negative E(r) corresponds to an
electric field pointing towards the origin, and positive
E(r) corresponds to a field
pointing away. What is E(r)...
3. a) Consider a point charge q at the center of an imaginary box with side lengths 2a. Explicitly calculate the flux of the electric field through the box and show that it agrees with Gauss's law b) Suppose the electric field of a point charge q is proportional to 1/r3 instead of 1/r2. Does Gauss's law hold in this case? Hint: compute the electric fluz through a sphere centered at the location of q. Is your answer dependent on...
3. a) Consider a point charge q at the center of an imaginary box with side lengths 2a. Explicitly calculate the flux of the electric field through the box and show that it agrees with Gauss's law. b) Suppose the electric field of a point charge q is proportional to 1/r3 instead of 1/2. Does Gauss's law hold in this case? Hint: compute the electric flur through a sphere centered at the location of q. Is your answer dependent on...
Summary 583 Bridging Problem An imaginary sphere of radius R is centered at the origin, as shown in Pigure 17,37. A charge q is rigidly fixed to the x axis at +R/2 and a second charge g is at-R2. Finally, a proton (of mass and charge te) is released from rest oa the y axis. in terms of e, m, R of the proton at the moment it is released from y +R/4. (b) What are the magnitude and direction...
3). A thin spherical shell is centered at the origin with radius 1.8 meter. The shell has a surface charge density of -5 C/m². At the center of the spherical shell (at the origin) there is a +2 C point charge. Calculate the magnitude of the electric field at 1.2 meters from the center of the spherical shell.
4. A spherically sym metric charge distribution has the following radial dependence for the volume charge density ρ 0 if r > R where γ is a constant a) What units must the constant y have? b) Find the total charge contained in the sphere of radius R centered at the origin. c) Use the integral form of Gauss's law to determine the electric field in the region r < R. (Hint: if the charge distribution is spherically symmetric, what...
Only part f) please!
4 A spherically symmetric charge distribution has the following radial dependence for the volume charge density ρ ρ(r) If r > R where y is a constant a) What units must the constant y have? b) Find the total charge contained in the sphere of radius R centered at the origin c) Use the integral form of Gauss's law to determine the electric field in the region r < R. Hint: if the charge distribution is...
A sphere of radius R is centered at the origin. A constant magnetic field of magnitude B is in the +k direction. What is the value of the magnetic flux that passes through the hemispherical surface that has z<0? (This is the half of the surface of the sphere in the region z<0.) Define the flux to be positive if it points from the inside of the sphere to the outside. a) 2 B b) -2B c) - TPB d)...
8) A Gaussian spherical surface of radius 0.20 m completely surrounds a collection of charges. A uniform electric field emerging from the charges has a value of.51 NC. a) Find the electric flux through the surface if the collection consists of a single charge. Use the Gauss Law to determine the magnitude of this charge inside the sphere. b)
A hollow sphere of radius a has uniform
surface charge density σ and is centered at the origin. It
sits inside a bigger sphere, also centered at the origin, with
radius b > a and uniform
surface charge density −σ. Because of the spherical
symmetry, the electric field will have the form () =
E(r) r̂, where
negative E(r) corresponds to an
electric field pointing towards the origin, and positive
E(r) corresponds to a field
pointing away. What is E(r)...
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