`(i)` If two similar large plates, each of area A having surface charge densities `+sigma` and `-sigma` are separated by a distance `d` in air,find the expression for
`(a)` field at points between the two plates and on outer side of the plates. Specify the direction of the field in each case.
`(b)` the potential difference between the plates.
`(c)` the capacitance of the capacitor so formed.
`(ii)` Two metallic spheres of radii `R` and `2R` are charged so that both of these have same surface charge density `sigma`. If they are connected to each other with a conducting wire, in which direction will the charge flow and why ?

Explanation

`(i) (a)` In region `I : E=-sigma//2in_(0)+sigma//2in_(0)=0`
In region `II : E=sigma//2in_(0)+sigma//2in_(0)=sigma//in_(0)`(towards right)
In region `III : E=sigma//2in_(0)-sigma//2in_(0)=0`
`(b) V=Ed=(sigma)/(in_(0))d`.
`(c ) C=q//V=(q in_(0))/(sigmad)=(qin_(0)A)/(qd)=(in_(0)A)/(d)`
`(ii)` Charge on sphere with radius `R=4piR^(2)sigma`
Charge on sphere with radius `2R=4pi(4R^(2))sigma`
Potential on sphere with radius `R=(1)/(rpi in_(0))(4piR^(2)sigma)/(R )=(Rsigma)/(in_(0))`
Potential on sphere with radius `2R=(1)/(4pi in_(0))(4pi *4R^(2)sigma)/(PR)=(2Rsigma)/(in_(0))`
So, charge will flow later to former as potential of later is high.