You will use Gauss's Law to calculate the electric field inside a uniformly charged sphere of...

  
 
 

   

 

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You will use Gauss's Law to calculate the electric field inside a uniformly charged sphere of radius R. To be clear, the sphere has a constant volume charge density of p = Qtotal / Vtotal distributed uniformly throughout the sphere. a) Find the charge enclosed by a spherical Gaussian surface of radius r < R centered on the center of the sphere. R 2D cross-section of sphere b) Calculate the electric flux for the spherical Gaussian surface of radius r < R, centered on the sphere. Hint: the charge distribution has spherical symmetry. What does this tell you about the direction of the electric field at the Gaussian surface? What does this tell you about the magnitude of the electric field at the Gaussian surface? c) Use Gauss's Law to determine the magnitude of the electric field. What direction is it pointing? Hint: Gauss's law states that your answer for part a is proportional to your answer for part b. The proportionality factor is the vacuum permittivity --- make sure you have it in the right place according to Gauss's law. d) What is the electric field outside of the sphere? Recall that the electric field outside of a uniform sphere of charge is equal to the electric field of a point charge of the same magnitude. e) Using your results for c and d, draw a graph of the magnitude of the electric field as a function of radius r. Hint: the behavior of the electric field changes at r = R. You will use Gauss's Law to calculate the electric field inside a uniformly charged sphere of radius R. To be clear, the sphere has a constant volume charge density of p = Qtotal / Vtotal distributed uniformly throughout the sphere. a) Find the charge enclosed by a spherical Gaussian surface of radius r < R centered on the center of the sphere. R 2D cross-section of sphere b) Calculate the electric flux for the spherical Gaussian surface of radius r < R, centered on the sphere. Hint: the charge distribution has spherical symmetry. What does this tell you about the direction of the electric field at the Gaussian surface? What does this tell you about the magnitude of the electric field at the Gaussian surface? c) Use Gauss's Law to determine the magnitude of the electric field. What direction is it pointing? Hint: Gauss's law states that your answer for part a is proportional to your answer for part b. The proportionality factor is the vacuum permittivity --- make sure you have it in the right place according to Gauss's law. d) What is the electric field outside of the sphere? Recall that the electric field outside of a uniform sphere of charge is equal to the electric field of a point charge of the same magnitude. e) Using your results for c and d, draw a graph of the magnitude of the electric field as a function of radius r. Hint: the behavior of the electric field changes at r = R.