The ink drops have a radius of 18.0 μm and leave the nozzle and travel toward the paper at a velocity of 20.0 m/s . The drops pass through a charging unit that gives each drop a positive charge q by causing it to lose some electrons. The drops then pass between parallel deflecting plates of length 1.50 cm where there is a uniform vertical electric field with a magnitude of 7.75×104 N/C .
If a drop is to be deflected a distance of 0.350 mm by the time it reaches the end of the deflection plate, what magnitude of charge must be given to the drop? (Assume that the density of the ink drop is 1000kg/m3).
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So I did F = Eq and F = ma to get
a = Eq//m
then I used kinematics and set
1/2at^2 replacing a to get 1/2 * (qE/m) * t^2
therefore q = (2 * d * m) / (E * t2)
but I keep getting
1.6057347713e−13 C which is wrong
To find the magnitude of charge, we can use the relationships you mentioned: F = Eq and F = ma. Let's break down the steps to solve the problem correctly:
1. Start with the equation F = Eq (force equals electric field multiplied by charge).
2. Rearrange the equation to solve for charge: q = F/E.
3. Next, we need to find the force experienced by the drop. The only force acting on the drop is its weight:
F = mg, where m is the mass of the drop and g is the acceleration due to gravity (approximately 9.81 m/s^2).
4. Calculate the mass of the drop using its volume and density:
The volume of the drop can be calculated using the formula for the volume of a sphere: V = (4/3)πr^3, where r is the radius
(given as 18.0 μm, or 18.0 x 10^-6 m).
The mass can be found using the density of the ink drop (given as 1000 kg/m^3) and the volume calculated earlier: m = ρV.
5. Substitute the mass and the acceleration due to gravity into the force equation to find the force acting on the drop: F = mg.
6. Plug the values of force and electric field into the equation for charge: q = F/E.
7. Convert the distance of deflection to meters (from 0.350 mm to 0.350 x 10^-3 m) and divide it by the velocity of the drop (given as 20.0 m/s) to find the time taken (t) by the drop to pass the plates.
8. Finally, substitute the values of force, electric field, mass, and time into the equation for charge: q = (F/E) x t^2.
By following these steps correctly, you should be able to obtain the correct magnitude of charge for the drop.