Two small charged spheres contain charges -q1 and -q2 respectively-A charge dqis remived from -q1 and transferred to -q2-Find charge on each sphere for maximum electric force between them-

Let #160;q' #160;be #160;the #160;chage #160;which #160;is #160;transfered #160;from #160;sphere #160;containing #160;charge #160;q1 # ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard VIII

Physics

Electrostatic Induction

Two small cha...

Question

Two small charged spheres contain charges +q₁ and +q₂ respectively.A charge dqis remived from +q₁ and transferred to +q₂.Find charge on each sphere for maximum electric force between them.

Open in App

Solution

$L e t q' b e t h e c h a g e w h i c h i s t r a n s f e r e d f r o m s p h e r e c o n t a i n i n g c h a r g e q_{1} t o a n o t h e r s p h e r e h a v i n g c h a r g e q_{2}, S o E l e c t r o s t a t i c F o r c e, F = \frac{(q_{1} - q') (q_{2} - q')}{4 π ε_{0} r^{2}} F o r m a x i m u m F o r c e, \frac{d F}{d q'} = 0, \frac{d^{2} F}{d q'^{2}} < 0 \frac{d F}{d q'} = \frac{- q_{2} - q_{1} - 2 q'}{4 π ε_{0} r^{2}} = 0 \Rightarrow q' = \frac{1}{2} (q_{1} + q_{2}) S o c h a g e o n 1 s p h e r e = \frac{(q_{1} + q_{2})}{2}, o n 2 s p h e r e = \frac{(q_{1} + q_{2})}{2},$

Suggest Corrections

Similar questions

Two uniformly charged spheres with radii $r_{1}$ & $r_{2}$ and charges $Q_{1}$ & $Q_{2}$ are separated by distance d (from the periphery of the two spheres). What is the magnitude of force on $Q_{2}$ due to $Q_{1}$ ?

Q. A point charge

q_{1}

exerts an electric force on a second point charge

q_{2}

. If a third charge

q_{3}

is brought near to

q_{2}

, the electrostatic force exerted by

q_{1}

q_{2}

will
(Presence of charges in the vicinity does not change the force between any two charges)

Q. Point charges

q_{1}

and

q_{2}

are placed in air at a distance 'r'. The ratio of the force on charge

q_{1}

by charge

q_{2}

and force on charge

q_{2}

by charge

q_{1}

is?

Q. For the given charge configuration consisting of charges

+ q_{1}

and

+ q_{2}

such that

q_{1} > q_{2}

, the relation between flux through two imaginary spheres

S_{1}

and

S_{2}

as shown in the figure will be

Q. Fill in the blank :

The mutual electrostatic force between two point charges

q_{1}

and

q_{2}

is _____ to the product of charges

q_{1}

and

q_{2}

Join BYJU'S Learning Program

Two small charged spheres contain charges +q1 and +q2 respectively.A charge dqis remived from +q1 and transferred to +q2.Find charge on each sphere for maximum electric force between them.

Let q' be the chage which is transfered from sphere containing charge q1 to another sphere having charge q2,So Electrostatic Force,F=(q1-q')(q2-q')4πε0r2For maximum Force ,dFdq'=0,d2Fdq'2<0dFdq'=-q2-q1-2q'4πε0 r2=0⇒q'=12(q1+q2)So chage on 1 sphere=(q1+q2)2, on 2 sphere=(q1+q2)2,

Two small charged spheres contain charges +q₁ and +q₂ respectively.A charge dqis remived from +q₁ and transferred to +q₂.Find charge on each sphere for maximum electric force between them.