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What is the force between two small char...

What is the force between two small charged spheres having charges of `2xx10^(-7)C and 3xx10^(-7) C` placed 30cm apart in air ?

A

`6 xx 10^(−4)` N

B

`6 xx 10^(−3)` N

C

`6 xx 10^(−6)` N

D

`5 xx 10^(−3)` N

Text Solution

Verified by Experts

The correct Answer is:
B
Repulsive force of magnitude `6 xx 10^(−3) N`
Charge on the first sphere, `q_(1) = 2 xx 10^(−7) C`
Charge on the second sphere, `q_(2) = 3 xx 10^(−7) C`
Distance between the spheres, `r = 30 cm = 0.3 m`
Electrostatic force between the spheres is given by the relation,
`F=(q_(1)q_(2))/(4 piepsilon_(0) r^(2))`
Where, ` epsilon_(0)` = Permittivity of free space
`(1)/((4 piepsilon_(0)) = 9 xx 10^(9) Nm^(2) C^(-2)`
`F = (9 xx 10^(9) xx 2 xx 10^(-7) xx 3 xx 10^(-7))/((0.3)^(2)) = 6 xx 10^(-3)N`
Hence, force between the two small charged spheres is `6 xx 10^(−3)` N. The charges are of same nature. Hence, force between them will be repulsive.
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Knowledge Check

  • The force between two small charged spheres having charges of 1xx10^(-7)C and 2xx10^(-7)C placed 20 cm apart in air is

    A
    `4.5xx10^(-2)N`
    B
    `4.5xx10^(-3)N`
    C
    `5.4xx10^(-2)N`
    D
    `5.4xx10^(-3)N`

  • The potential at a point due to charge of 5xx10^(-7)C located 10 cm away is

    A
    `3.5xx10^(5)V`
    B
    `3.5xx10^(4)V`
    C
    `4.5xx10^(4)V`
    D
    `4.5xx10^(5)V`

  • Two metallic spheres of radii 1 cm and 3 cm are given charges of -1 xx 10^(-2) C and 5 xx 10^(-2) C , respectively . If these are connected by a conducting wire , the final charge on the bigger sphere is

    A
    ` 2 xx 10^(-7) C `
    B
    `3 xx 10^(-2) C`
    C
    `4 xx 10^(-2) C `
    D
    `1 xx 10^(-2) C `

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