The polar molecule in the diagram below has a positive charge of +19e at one end
ID: 1413224 • Letter: T
Question
The polar molecule in the diagram below has a positive charge of +19e at one end and a negative charge of -19e at the other. It is immersed in a nonuniform electric field (and aligned with the “local” field direction). At the negative end of the molecule the field is given by the vector E = ?1.41×107 N C*i + 3.65 ×106 N C*j . It points in the same direction at the positive end, but its magnitude has been reduced by 3%.
a) Determine and express in unit vector notation the electric force that acts on each end of the molecule. Determine the net electric force that acts on the molecule as a whole and express this vector in unit vector notation. Determine the magnitude of the net force vector and the angle it makes with the positive x axis.
b) How does the direction of the electric field vector compare to the direction of the net force? Briefly explain how you know.
c) What would be the net force on the molecule if the field were uniform and described everywhere around the molecule by the vector given. Explain/show how you know.
d) Water is a polar molecule, and in class it was shown that both the PVC and plexiglass pipes (charged) will bend a stream of water. (Here’s a youtube reference for the same thing: https://www.youtube.com/watch?v=VhWQ-r1LYXY). Based on the analysis you’ve just carried out, how could this experiment be used to distinguish a uniform electric field from a nonuniform field? Explain how you know.
1H Phy 2202 (Bradley-Hutchison)page-1-Explanation / Answer
a)
q=19e
E = 1.41×10^7 N C*i + 3.65 ×10^6 N C*j
Ereduced3%=-1.368×10^7 N C*i + 3.5405 ×10^6 j
Net force= (Ereduced3% * q) - (E * q)
Ereduced3% * q = (-1.368×10^7 N C*i + 3.5405 ×10^6 j) * 19*1.6*10^-19
Ereduced3% * q =(-41.587x10^-12 i + 10.763 x 10^-12 j )N
E * q = (- 42.864x10^12 i + 11.096x10^-12 j)N
Net force =(-41.587x10^-12 i + 10.763 x 10^-12 j )N -(- 42.864x10^12 i + 11.096x10^-12 j)N
Net force= (1.277x10^-12 i -0.333x10^-12 j )N in direction opposite to the field.
b) The electric field vector oposses opposes to the Net force vector. They have opposite direction in each of their components.
c) For a uniform field, the net force would be 0.
d) If the water molecule accelerates in this field, the field is non- uniform because a net force then acts on it. If no net force acts, the field is uniform.
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