In Elements of Electromagnetics, Sadiku, 6th Ed, Ex 4.3, pg 115-116. How is QE =

Question

In Elements of Electromagnetics, Sadiku, 6th Ed, Ex 4.3, pg 115-116. How is QE = m d^2x/dt^2 ax determined?

A practical application of electrostatics is in electrostatic separation of solids. For Florida phosphate ore, consisting of small particles of quartz and phosphate rock, can be separated into its components by applying a uniform electric field as in Figure 4.4. Assuming zero initial velocity and displacement, determine the separation between the particles after falling 80 cm. Take E-500 kV/m and Q/m= 9uSkg for both positively and negatively charged partiles example, EXAMPLE 4.3 FIGURE 4.4 Electrostatic separation of solids, for Example 4.3. +0 + O +O +O 0+ Quartz Phosphate

Explanation / Answer

We know the equation for the force acting on the body I.e Force(F)=mass(m) x acceleration (a) which is equal to the electrical field strength E=ma

According to coulombs the distance between two particles is directly proportional to the square of the distance between them.

Hence here the two particles are separated by some distance dx/dt.so charge Q=d^2x/dt

Thus electrostatic force is the product of the field strength and the charge.

Thus Q×E=d^2x/dt x ma

I.e QE=md^2x/dt a

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