Home
Class 12
PHYSICS
Two metal spheres ("radii" r1, r2 "with"...

Two metal spheres `("radii" r_1, r_2 "with" r_1 lt r_2)` are very far apart but are connected by a thin wire. If their combined charges is Q, then what is their common potential ?

A

`k Q//(r_1 + r_2)`

B

`kQ//(r_1 - r_2)`

C

`-k Q//(r_1 + r_2)`

D

`-kQ//r_1 r_2`

Text Solution

Verified by Experts

The correct Answer is:
a
`V_C = V_1 = V_2`
`(kq_1)/r_(1) = (kq_2)/r_(1)`
`q_(1)/q_(2) = r_(1)/r_(1)` …(i)
`q_1 + q_2 = Q` …(ii)
From Eqs. (i) and (ii), we get
`q_1 = (Q r)/(r_1 + r_2)`
Putting `V_(1)`, we get
`V_(C )=(kQ)/(r_(1)-r_(2))`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • ELECTRIC POTENTIAL

    CENGAGE PHYSICS|Exercise Multiple Correct|10 Videos

  • ELECTRIC POTENTIAL

    CENGAGE PHYSICS|Exercise Comprehension|31 Videos

  • ELECTRIC POTENTIAL

    CENGAGE PHYSICS|Exercise Subjective|28 Videos

  • ELECTRIC FLUX AND GAUSS LAW

    CENGAGE PHYSICS|Exercise MCQ s|38 Videos

  • ELECTRICAL MEASURING INSTRUMENTS

    CENGAGE PHYSICS|Exercise M.C.Q|2 Videos

Similar Questions

Explore conceptually related problems

Two metallic s pheres of radii R_(1) and R_(2) are connected b y a thin wire. If +q_(1)~ and +q_(2) are the charges on the two s pheres then

Two equally charged spheres A and B with radii r_(A) and r_(B)(r_(A) gt r_(B)) are connected by a conducting wire. Will the charge density on both the spheres become equal after connection?

Knowledge Check

  • Two conducting spheres of radii r_(1) and r_(2) having charges Q_(1) and Q_(2) respectively are connected to each other. There is

    A
    no change in the energy of the system
    B
    an increase in the energy of the system
    C
    always a decrease in the energy of the system
    D
    a decrease in the energy of the system unless `Q_(1)r_(2)=Q_(2)r_(1)`

  • Surface charge densities of two thin concentric spherical capacitors or shells are given as sigma and -sigma . The radii are R and 2R. The concentric capacitors are connected by a thin conducting wire. The entire charge on the inner miner transfers to the outer caspacitor and potential difference between them becomes zero. final potential of each capacitor will be

    A
    `-(3sigmaR)/(2epsi_(0))`
    B
    `-(2sigmaR)/(epsi_(0))`
    C
    `-(sigmaR)/(2epsi_(0))`
    D
    zero

  • Two isolated charged metallic spheres of radii R_(1) and R_(2) having charges Q_(1) and Q_(2) respectively are connected to each other, then there is-

    A
    No change in the electrical energy of the system
    B
    An increase in the electrical energy of the system
    C
    Always a decrease in the electrical energy of the system
    D
    A decrease in electrical energy of the system until `Q_(1) R_(2)= Q_(2)R_(3)`

    • Similar Questions

    Explore conceptually related problems

    Two concentric spherical conducting shells of radii r and R (r lt R ) carry charges q and Q respectively . The two shells are now connected by a conducting wire. The final charge on the inner shell is

    Two charged metallic spheres of radii r_(1) and r_(2) are touched and separated. Calculated the ration of their (i) Charges (ii) Potential (ii) Self energy (iv) Electric field at the surface (v) Surface cahrge density

    Two spherical conductors of radii R, and R2 (R2 > Ri) are charged. If they are connected by a conducting wire, find out the ratio of the surface charge densities on them.

    two metal spheres of radii R_(1) and R_(2) are charged to the same potential. The ratio of charges on the spheres is

    The insulated spheres of radii R_(1) and R_(2) having charges Q_(1) and Q_(2) respectively are connected to each other. There is

    Home
    Profile