Problem 2.20 One of these is an impossible electrostatic field. Which one? (a) E= k[xy x + 2yzý + 3xz2]; (b) E = k[y² + (2xy + z²) ý + 2yz 2). Here k is a constant with the appropriate units. For the possible one, find the potential, using the origin as your reference point. Check your answer by computing VV. [Hint: You must select a specific path to integrate along. It doesn't matter what path you choose, since the answer is path-independent, but you simply cannot integrate unless you have a particular path in mind.]
Rigid Body
A rigid body is an object which does not change its shape or undergo any significant deformation due to an external force or movement. Mathematically speaking, the distance between any two points inside the body doesn't change in any situation.
Rigid Body Dynamics
Rigid bodies are defined as inelastic shapes with negligible deformation, giving them an unchanging center of mass. It is also generally assumed that the mass of a rigid body is uniformly distributed. This property of rigid bodies comes in handy when we deal with concepts like momentum, angular momentum, force and torque. The study of these properties – viz., force, torque, momentum, and angular momentum – of a rigid body, is collectively known as rigid body dynamics (RBD).
![Problem 2.20 One of these is an impossible electrostatic field. Which one?
(a) Ek[xy x + 2yzý + 3xz2];
(b) E= k[y² + (2xy + z²) ŷ + 2yz 2].
Here k is a constant with the appropriate units. For the possible one, find the potential, using
the origin as your reference point. Check your answer by computing VV. [Hint: You must
select a specific path to integrate along. It doesn't matter what path you choose, since the
answer is path-independent, but you simply cannot integrate unless you have a particular path
in mind.]
Problem 2.11 Use Gauss's law to find the electric field inside and outside a spherical shell of
radius R, which carries a uniform surface charge density o. Compare your answer to Prob. 2.7.
Problem 2.21 Find the potential inside and outside a uniformly charged solid sphere whose
radius is R and whose total charge is q. Use infinity as your reference point. Compute the
gradient of V in each region, and check that it yields the correct field. Sketch V (r).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F866d9fde-2cb2-4ff0-8d56-5d19cdf2be25%2F9e622e2a-4ab9-4bde-a1bf-7f9d1d336a86%2F4m05h9q_processed.png&w=3840&q=75)
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