A natural water molecule (H2O) in its vapor state has an electric dipole moment of magnitude, p = 6.2 x 10-30 C. m. (a) Find the distance of the positive and negative charge centers of the molecule. Note that there are 10 electrons and 10 protons in a natural water molecule. (b) If the molecule is placed in a uniform electric field, E = 2 x 10' N/C find the maximum torque acting on the molecule. (c) How much work is needed to rotate this molecule by 180° in this field starting from the initial position, for which 0 = 0? Hint: 0 is the angle between the electric dipole moment and the electric field

a    

b    

c  

Explanation:

From the question we are told that

   The magnitude of electric dipole moment is  

     The electric field is

The distance between the positive and negative charge center is mathematically evaluated as

Where  e is the charge on one electron which has a constant value of  

  Substituting values

The maximum torque is mathematically represented as

Here  

This because at maximum the molecule is perpendicular to the field

    substituting values

The workdone is mathematically represented as

where   is the potential energy at 180° which is mathematically evaluated as

Where the negative signifies that it is acting against the  field

   substituting values

and

      is the potential energy at 0° which is mathematically evaluated as

   substituting values

So

jupiter is the largest planet in our solar system, having a mass and radius that are respectively, 318 and 11.2 times that of earth. suppose that an object falls from rest near the surface of each planet and that the acceleration due to gravity remains constant during the fall. each object falls the same distance before striking the ground. determine the ratio of the time of fall on jupiter to that on earth.

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