Q23 of 31 Page 6

Two charges q and –3q are placed fixed on x-axis separated by distance ‘d’. Where a third charge 2q should be placed such that it will not experience any force?

The charge +2q should be placed to the right of +q charge because if it is placed in between +q and -3q charge both will apply the force in same direction and should be placed close to +q charge because the magnitude is less as compare to +3q charge ,so distance should be less too.


Let suppose it is placed at distance x from +q as shown in fig 1.23 a.



Using Coulomb’s law,


The force on +2q Charge due to +q charge is = k


And the force on +2q Charge due to -3q charge is = k


Where K is Coulombs constant


i.e K= k = 9×109 N �m2 �C−2


So the net force on +2q charge will be



And according to question net force should be equal to zero.


∴


⇒


⇒ =


Simplifying it we will get the two value of x


⇒ =







Here,






Now,


x=


=


=


=


On rationalising we get,


=


=


=


On solving we get



Now we will exclude the negative value as we have discussed the +2q charge can’t be placed in between.


As d - will lie in between the charges.So we have to neglect the –ive value,


So


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21

Consider a coin of Example 1.20. It is electrically neutral and contains equal amounts of positive and negative charge of magnitude 34.8 kC. Suppose that these equal charges were concentrated in two point charges separated by (i) 1 cm , (ii) 100 m ( ∼length of a long building), and (iii) 106 m (radius of the earth). Find the force on each such point charge in each of the three cases. What do you conclude from these results?

 22

Fig. 1.10 represents a crystal unit of cesium chloride, CsCl. The cesium atoms, represented by open circles are situated at the corners of a cube of side 0.40nm, whereas a Cl atom is situated at the centre of the cube. The Cs atoms are deficient in one electron while the Cl atom carries an excess electron.


(i) What is the net electric field on the Cl atom due to eight Cs atoms?


(ii) Suppose that the Cs atom at the corner A is missing. What is the net force now on the Cl atom due to seven remaining Cs atoms?


 24

Fig. 1.11 shows the electric field lines around three point charges A, B and C.

(a) Which charges are positive?


(b) Which charge has the largest magnitude? Why?


(c) In which region or regions of the picture could the electric field be zero? Justify your answer.


(i) near A, (ii) near B, (iii) near C, (iv) nowhere.



 25

Five charges, q each are placed at the corners of a regular pentagon of side ‘a’ (Fig. 1.12).


(a) (i) What will be the electric field at O, the center of the pentagon?


(ii) What will be the electric field at O if the charge from one of the corners (say A) is removed?


(iii) What will be the electric field at O if the charge q at A is replaced by –q?


(b) How would your answer to (a) be affected if pentagon is replaced by n-sided regular polygon with charge q at each of its corners?