NCERT Physics Class 12 Exemplar Chapter 1 Electric Charges and Fields Part 9

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Q.23 Two charges and are placed fixed on x-axis separated by distance . Where a third charge should be placed such that it will not experience any force?

Solution:

Two charges at a distance

Two Charges at a Distance

Two charges at a distance

At P: on , Force due to is to the left and that due to is to the right.

( sign would be between and and hence is unacceptable.)

to the left of .

Q.24 Fig. shows the electric field lines around three point charges and .

Electric field due to charges

Electric Field Due to Charges

Electric field due to charges

Solution:

(a) Charges and are positive since lines of force emanate from them.

(b) Charge has the largest magnitude since maximum numbers of field lines are associated with it.

(c) (I) near . There is no neutral point between a positive and a negative charge. A neutral point may exist between two like charges. From the figure we see that a neutral point exists between charges and . Also between two like charges the neutral point is closer to the charge with smaller magnitude. Thus, electric field is zero near charge .

Q. 25 Five charges, each are placed at the corners of a regular pentagon of side (Fig.).

Charges at pentagon corners

Charges at Pentagon Corners

Charges at pentagon corners

(a) (I) What will be the electric field at , the centre of the pentagon?

(II) What will be the electric field at if the charge from one of the corners (say ) is

removed?

(III) What will be the electric field at if the charge at is replaced by ?

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

Solution:

(a)

(I) The point , the centre of the pentagon is equidistant from all the charges at the end point of pentagon. Thus, due to symmetry, the electric fields due to all the charges are cancelled out. As a result electric field at is zero

(II) We can write that the vector sum of electric field due to charge A and electric field due to other four charges at the centre of cube should be zero or.

Hence

When charge is removed from , net electric field at the centre due to remaining charges along .

(III) If charge at is replaced by , then electric field due to the negative charge

along .

Hence net electric field at the centre

along

(b) If pentagon is replaced by sided regular polygon with charge q at each of its comers Here again charges are symmetrical about the centre The net electric field at would continue to be zero, it doesn’t depend on the number of sides or the number of charges.