Question

Electric charges having same magnitude of electriccharge q' coulombs are placed at x = 1 m, 2 m.4 m. 8m ....... so on. If any two consecutivecharges have opposite sign but the first charge isnecessarily positive, what will be the potential atx=0​

Answer 1

Electric charges having same magnitude of electric charge q coulombs are placed at x = 1 m, 2 m, 4 m, 8m ....... so on. If any two consecutive charges have opposite sign but the first charge is necessarily positive.

electric potential due to charge place at (x = 1m) at origin , $V_1=\frac{kq}{1m}$

electric potential due to charge place at (x = 2m) at origin , $V_2=\frac{k(-q)}{2m}$

electric potential due to charge place at (x = 4m) at origin , $V_3=\frac{kq}{4m}$

electric potential due to charge place at (x = 8m) at origin , $V_4=\frac{k(-q)}{8m}$

......

..............

now net potential at origin , $V=V_1+V_2+V_3+V_4+......+V_n$

= $\frac{kq}{1}+\frac{k(-q)}{2}+\frac{kq}{4}+\frac{k(-q)}{8}+.....$

= $kq\left[1-\frac{1}{2}+\frac{1}{4}-\frac{1}{8}+....\right]$

here you see series : 1 - 1/2 + 1/4 - 1/8 .... are in geometric progression where a = 1 and r = -1/2

so, sum of infinite terms in GP , S = a/(1 - r) = 1/(1 + 1/2) = 2/3

hence, net potential at origin is $\frac{2}{3}kq$

Answer 2

Answer:

Potential due to a charge at distance r is  kq/r

Potential due to the + charge at distance 1m is  kq/1m

Potential due to the -charge at distance 4m is − kq/2m

​potential due to the the charge at distance 4m is  kq/4m

and so

The total is kq(1− 1/2 + 1/4 − 1/8 +..........)

The thing  inside parentheses is a geometeric series.

The sum of an infinite geometric senses is a (1−r)

where a = first term =1 and r=common ratio=-1/2

So, the infinite sum is  1 / (1−(− 1/2 )) = 1/ (3/2)

= 2/3

Thus the total potential is kq× 2/3

hope...this helps...please mark as brainliest.