Grade 12Electrostatics

A charge Q is divided into two parts of qand Q-q if the coulomb repulsion between them when they are seprated is to be maximum the ratio of Q/q should be

pallavi pradeep bhardwaj

16 Years agoGrade 12

10 Answers

Badiuddin askIITians.ismu Expert

16 Years ago

Dear pallavi

let parts are sepereted at a distance of d

so repulsion force F= k q(Q-q)/d²

here Q and d are constant so for maximum force differentiate the force w.r.t q

dF/dq = k/d²[Q -2q]

for maximum force dF/dq=0

Q-2q=0

Q/q =2

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Karthik Pasupulatei

11 Years ago

i cant understand how todifrentiate f w.r.t q

Hermione Weasley

10 Years ago

F = kq(Q-q)/r^2

=> F = k(Qq-q^2)/r^2

Since Q, r, and k are all constants,

Differentiating,

dF/dq = d (k(Qq-q^2)/r^2) / dq

=> dF/dq = k/r^2 * [Q – 2q]

Since the maximum force is a constant, dF/dq must be equal to 0.

Hence, k/r^2 * [Q – 2q] = 0

=> Q – 2q = 0

=> Q = 2q

=> q = Q/2 or Q/q = 2

Ashish Kumar

9 Years ago

Let q and Q-q be the charges on the two objects. Then force between the two object is F =1/ 4 pi Eò . q(Q-q)/ r^2 where r is the distance between them....For F to be max , dF/dq = 0 Or 1/4pi E0 .r^2 .d(qQ-q^2)/ dq= 0 Q-2q =0 q = Q/2 answer....

Leena Surendran

9 Years ago

I dI`d not understand the part where the maximum force is a constant. And why did you equate dF/dq to zero?

Deepti

8 Years ago

We equate dF/dq=0 because it`s one of the rules of differentiation where we equate it to 0 when we want any maximum or minimum value of something

Shailendra Kumar Sharma

8 Years ago

q and (Q-q) be charges
So the force (F) =Kq(Q-q)/r2
To maximize dF/dq=0
so (q-Q+q=0)

q=Q/2
in other words, two charge force will increase as the multiple will increase, but when the multiple will be maximum at the mid point only.

Om Jadhav

7 Years ago

I did not understand that On place of (qQ-q^2/d^2) how (Q-2q)/d^2 came.

Can you please explain me

Please answer earlier

Kshitish Sorte

7 Years ago

Differentiating gives us the local maxima(maximum value) and minima(minimum value) of a curve. So I guess that's why we differentiate.

Rishi Sharma

6 Years ago

Hello Pallavi,
let parts are sepereted at a distance of d
so repulsion force F= k q(Q-q)/d2
here Q and d are constant so for maximum force differentiate the force w.r.t q
dF/dq = k/d2 [Q -2q]
for maximum force dF/dq=0
Q-2q=0
Q/q =2
Thanks
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