A particle with a charge of 22.0 µC is at the center of a thin spherical shell of radius R = 13.0 cm that has uniform surface charge density o. Determine the value of o such that the net electric field outside the shell is zero. C/m2
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- Suppose we have a charge, q1=3 μC. This charge makes an electric field some distance r=69 cm away from it. Now suppose our measurement of q1 is only accurate to within 0.1 μC, and our measurement of r is only accurate to within 1 cm. a)If we were to calculate the electric field made by that charge at the indicated distance, what would be the uncertainty in our calculation due only to the uncertainty in the size of q1? b)What is the uncertainty in our field calculation due only to the uncertainty in the charge separation r? c)What is the total uncertainty in our electric field calculation due to the uncertainty in the size of q1 and the uncertainty in the charge separation r?You are an astronaut, living for a long time interval in the International Space Station (ISS). During your off-duty hours, you have run out of books to read and video games to play. So, your mind wanders to your hobby of music. The last book you read discussed Gauss's law, and you get an inspiration. You plan to attach two nonconducting spheres of radius r = 1.50 cm together using a light insulating string of length L and linear mass density μ = 5.00 x 10-3 kg/m, with the string attached at the surface of each sphere. Then, using the electrical system on the ISS, you will be able to electrify each sphere to a charge of Q = 75.0 μC, uniformly spread over the surface of the sphere. The combination will then be allowed to float freely in the ISS. The spheres will repel, creating a tension in the string. When you pluck the string, you wish it to play a perfect middle C, at 262 Hz. Determine the length of the string (in cm) that you need. (Assume the frequency of 262 Hz is the fundamental…Directions: Assume, unless otherwise specified, that all numbers have at least 3 significant figures. You may work together, but make sure that you are working--not just watching. The magnitude of the force of attraction between the proton and electron in a hydrogen atom is: F = where e is the magnitude of the charge, k is a constant, and r is the radius of the circular orbit. Assume the proton is fixed in place and the electron is in a circular orbit of radius ri. The electron then "jumps" to a new, smaller radius r2. What is the change in the total mechanical energy of the system (in terms ri, r2, e, and k)? Hint: Use dynamics to calculate the kinetic energy for the electron in the initial and final orbits, then calculate the potential energy in both orbits (you will need to develop an expression for the potential energy and remember the force is attractive). Do you know what form the change in mechanical energy takes?
- A coaxial cylinder of length L = 5 m consists of two cylindrical shells of radii a = 15 cm and b = 20 cm, respectively (see figure). The charge of the inner cylinder shell is Q = + 17.7 μC while the outer shell charge is Q = -17.7 μC. Find the electric field strength at: rc = 10 cm, rd = 18 cm, and re = 25 cm! Please write your answer neatly and readable as well :)Discuss the role that symmetry plays in the application of Gauss’s law. Give examples of continuous charge distributions in which Gauss’s law is useful and not useful in determining the electric field.