Electric charges and fields

 

Electric Charges and Fields

 17-   Problems

Question1. A particle carrying charges +q is held at the center of a square of each side one meter. It is surrounded by eight charges arranged on the square as shown in the figure. If q= 2 μC, what is the net force on the particle?


Solution. As is clear from figure, force on the particle at 0 due to (-2q, -2q); (-3q,-3q) and (+4q, +4q) are equal and opposite. They cancel out in pairs. However, the force due to +7q and -7q add up. Therefore, the net force on the particle at 0 is


Question2. Coulomb’s law for the electrostatic force between two point charge and Newton’s law for gravitational force between two stationary point masses, both have an inverse square dependence on the distance between the charges/masses.

(a) Compare the strength of these forces by these forces by determining the ratio of their magnitude (1) for an electron and a proton (2) for two protons

(b) Estimate the acceleration for electron and proton due to the electrical force of their mutual attraction when they are 1A0 apart.



Question3. Two electrons and a positive charge q are held along a straight line. At what position and for what value of q will the system be in equilibrium? Check whether it is stable, unstable, or neutral equilibrium.



Solution. Let two-electron of charge –e each be held at A and B. The third charge +q must be placed at the center O of AB. The forces on +q, due to two electrons being equal and opposite, cancel each other and it is in equilibrium.

For the charge(-e) at A to be in equilibrium, in the above figure, the force on the charge at A due to –e charge at B +force on charge at A due to +q charge at O=zero.



If charge at O is moved slightly toward A. It would not return to O on its own and shall continue to move toward A. Hence equilibrium is unstable.

Question4. Two equal positive charges, each of 2μC interact with a third positive charge of 3μC situated as shown in the figure. Calculate the magnitude and direction of the force on the 3μC charges.



Solution. In above figure

                                    OA = OB = 3m, OP = 4m

According to coulomb’s law,

Force on charge at P due to charge at A



F1 = 2.16 × 10-3 N, along with PA’, opposite to PA. It has two rectangular componetsF1 cos  along with PX and F1 sin  along with PY’. Similarly, the force on the charge at P due to charge at B, F2 = F1 (in magnitude). It is along PB’ opposite to PB. It also has two rectangular components: F2 cos  along with PX and F2 sin along with PY.                                  

 The components along with PY and PY’ cancel. The components along PX add up.

 The total force on 3 μC charges is

Question5. Find the magnitude of the resultant force on a charge of 1μC held at P due to two charge of +2×10-8C and -10-8C at A and B respectively.



In given figure                             AP = 10cm and BP = 5cm.

                                                    ∠APB = 900



Question6. Consider three charges q1, q2, q3 each equal to q at the vertices of an equilateral triangle of side l. What is the force on a charge Q (with the same sign as q) placed at the centroid of the triangle?


Solution. As shown in given figure, draw AD⊥BC.


Question7. Consider the charges q, q, and – q placed at the vertices of an equilateral triangle of each side l. what is the force on each charge?




Question8. Two fixed point charges +4e and +e units are separated by a distance a. Where should the third point charge be placed for it to in equilibrium?



Question9. Two pieces of copper, each weighing 0.01 kg are placed at a distance of 0.1m from each other. One electron from per 1000 atom of one piece of transfer to other pieces of copper. What will be the Coulomb force between two pieces after the transfer of electron? The atomic weight of copper is 63.5g/mole. Avogadro’s number = 6.25 × 1023 / gram mole.


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