Given: a spherically symmetrical variable charge distribution p(r) = cr for r < (or equal to)...
Given: a spherically symmetrical variable charge distribution p(r) = cr for r < (or equal to) b and p = 0 elsewhere, and where c is a constant (units C/m^4), and r is the radial distance from the center of the distribution. Use Gauss’s Law to obtain a mathematical expression for the electric field (a) for r < b; (b) r > b; and (c) show that the two expression give the same value for the electric field at the boundary r = b.
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Given: a spherically symmetrical variable charge distribution
p(r) = cr for r < (or equal to)...
A nonuniform, but spherically symmetric, distribution of charge has a charge density ρ(r) given as follows:...
A nonuniform, but spherically symmetric, distribution of charge has a charge density ρ(r) given as follows: ρ(r)=ρ0(1−r/R) for r≤R ρ(r)=0 for r≥R where ρ0=3Q/πR3 is a positive constant. Part A Find the total charge contained in the charge distribution. Express your answer in terms of some or all of the variables r, R, Q, and appropriate constants. Part B Obtain an expression for the electric field in the region r≥R. Express your answer in terms of some or all of...
Problem 3: In a certain region, a charge distribution exists that is spherically symmetric but nonuniform....
Problem 3: In a certain region, a charge distribution exists that is spherically symmetric but nonuniform. That is, the volume charge density p(r) depends on the distancer from the center of the distribution but not on the spherical polar angles and . The electric potential V(r) due to this charge distribution is V(r) = Pop (1-3(E)? +2(3) forrsa; and V(r) = 0 for r > a, where po is a constant having units of C/m' and a is a constant...
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...
4 A spherically symmetric charge distribution has the following radial dependence for the volume charge density...
4 A spherically symmetric 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 γ 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 can you say...
Consider a charged sphere of radius R. The charge density is not constant. Rather, it blows...
Consider a charged sphere of radius R. The charge density is not constant. Rather, it blows up at the center of the sphere, but falls away exponentially fast away from the center, p(r)=(C/r2)e-kr where C is an unkown constant, and k determines how fast the charge density falls off. The total charge on the sphere is Q. a) Write down the Electric Field outside the sphere, where r ≥ R, in term of the total Q. b) Show that C=...
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...
Please ignore written Work. Write out answer clearly. Thanks ·A spherically symmetric charge distribution ?(r) given...
Please ignore written Work. Write out answer clearly. Thanks
·A spherically symmetric charge distribution ?(r) given as follows: for rè R R'is a positive constant. Calculate the electric field E for rs Rand rR. (-points) 2.pr)- Where p 30/r E at reR is zero (O because p)0
A spherically symmetric charge distribution produces the electric field E⃗ =(250/r)r^N/C, where r is in m....
A spherically symmetric charge distribution produces the electric field E⃗ =(250/r)r^N/C, where r is in m. What is the electric field strength at r = 20.0 cm? What is the electric flux through a 15.0-cm-diameter spherical surface that is concentric with the charge distribution?
In reality, the magnitude of the force between the two spherically symmetrical charge distributions is described...
In reality, the magnitude of the force between the two spherically symmetrical charge distributions is described by Coulomb’s law F= (kq1q2)/d^2 where k is a constant equal to 8.99×109 Nm2/C2, q1 and q2 are the magnitudes of the charges, and d is the distance between the centers of the spheres. Assuming that both spheres have equal charges, estimate the charge on each sphere, using the first data point in your table. Remember that, for the calculations to be correct, both...
3. (20) A spherically symmetric charge distribution creates the following electric field (2) E E,r with...
3. (20) A spherically symmetric charge distribution creates the following electric field (2) E E,r with 20 r r < a for 4meoa3 (3) E,= Q 4mor2 for r> a where Q and a are positive constants of suitable units. (a) Draw a graph of E, for 0 <r3a; please label your graph clearly (b) Calculate the charge distribution that generates this electric field. (c) Draw a graph of the charge distribution for 0 <r< 3a; please label your graph...
Problem 3: In a certain region, a charge distribution exists that is spherically symmetric but nonuniform. That is, the volume charge density p(r) depends on the distancer from the center of the distribution but not on the spherical polar angles and . The electric potential V(r) due to this charge distribution is V(r) = Pop (1-3(E)? +2(3) forrsa; and V(r) = 0 for r > a, where po is a constant having units of C/m' and a is a constant...
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...
4 A spherically symmetric 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 γ 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 can you say...
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...
Please ignore written Work. Write out answer clearly. Thanks
·A spherically symmetric charge distribution ?(r) given as follows: for rè R R'is a positive constant. Calculate the electric field E for rs Rand rR. (-points) 2.pr)- Where p 30/r E at reR is zero (O because p)0
3. (20) A spherically symmetric charge distribution creates the following electric field (2) E E,r with 20 r r < a for 4meoa3 (3) E,= Q 4mor2 for r> a where Q and a are positive constants of suitable units. (a) Draw a graph of E, for 0 <r3a; please label your graph clearly (b) Calculate the charge distribution that generates this electric field. (c) Draw a graph of the charge distribution for 0 <r< 3a; please label your graph...
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