Answer to Question #132405 in Mechanics | Relativity for Jessica

Question #132405
A tiny ball (mass = 0.010 kg) carries a charge of -22 uC. What is the electric field magnitude that would cause the ball to float above the ground?
1
Expert's answer
2020-09-17T14:30:31-0400

Let's imagine that we have frame (X,Y). There are two forces acting on the body: gravity which is directed down (in Y- direction) and Lorenz force that is directed up (in Y+ direction). If we change field direction the ball will fall on the ground even faster, so the only possible direction of the Lorenz force to keep ball above the ground is Y+ direction.

According to the second Newton's law,

ma=F=qEmg\displaystyle m a = \sum F = qE - mg (signs here are according to the directions of the forces)

qEmg=0qE - mg = 0 since the ball is in equilibrium (a = 0).

E=mgq=0.0109.8122=0.00446  V/m4.5103  V/m\displaystyle E = \frac{mg}{q} = \frac{0.010 \cdot 9.81}{22} = 0.00446 \; \textrm{V/m} \approx 4.5 \cdot 10^{-3}\;\textrm{V/m}.

Answer: 4.5103V/m4.5 \cdot 10^{-3} V/m


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