Concept explainers
(a)
The charge on the sphere.
(a)
Explanation of Solution
Given:
The radius of the microsphere is
The Magnitude of electric field is
The magnitude of the drag force is
The viscosity of the air is
The density of the polystyrene is
Formula used:
Write the expression for the downward and upward force.
Here,
Write the expression for the force.
Here,
Write the expression for the mass.
Here,
Substitute
Write the expression for the charge.
Here,
Write the expression for the volume of the sphere.
Here,
Substitute
Solve the above equation for
Calculation:
Substitute
Conclusion:
Thus, the charge on the sphere is
(b)
The number of excess electron on the sphere.
(b)
Explanation of Solution
Given:
The radius of the microsphere is
The Magnitude of electric field is
The magnitude of the drag force is
The viscosity of the air is
The density of the polystyrene is
Formula used:
Write the expression for the downward and upward force.
Here,
Write the expression for the force.
Here,
Write the expression for the mass.
Here,
Substitute
Write the expression for the charge.
Here,
Write the expression for the volume of the sphere.
Here,
Substitute
Solve the above equation for
Calculation:
Substitute
Conclusion:
Thus, the number of excess electron on the sphere is 3.
(c)
The new terminal speed.
(c)
Explanation of Solution
Given:
The radius of the microsphere is
The Magnitude of electric field is
The magnitude of the drag force is
The viscosity of the air is
The density of the polystyrene is
Formula used:
Write the expression for the forces when electric field is upward.
Here,
Write the expression for the force.
Here,
Write the expression for the mass.
Here,
Substitute
Solve the above equation for
Calculation:
Substitute
Conclusion:
Thus, the new terminal speed is
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