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In a regular polygon of n sides, each co...

In a regular polygon of `n` sides, each corner is at a distance `r` from the centre. Identical charges are placed at `(n-1)` corners. At the centre, the intensity is `E` and the potential is `V`. The ratio `V//E` has magnitude

A

rn

B

`r(n-1)`

C

`(n-1)//r`

D

`r(n-1)//n`

Text Solution

Verified by Experts

The correct Answer is:
B
At the centre, the intensity is effectively due to one charge and the potential is due to `(n -1)` charges.
`therefore E = (KQ)/(r^(2)) and V = (k(n-1)Q)/(r)`
Hence `(V)/(E ) = (k (n-1)Q)/(r) xx (r^(2))/(kQ) = (n-1) r`
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Knowledge Check

  • In a regular polgyon of n sides, each cormer is at a distance r from the center . Identical chargs are placed at ( n-1) corners . At the center, the intensity is E and the potential is VM . The ratio V//E has magnitude .

    A
    ` r n`
    B
    ` r (n -1)`
    C
    ` (n -1) //r`
    D
    ` r(n -1) //n`

  • In a regular polygon of n sides, each corner is at a distance r from the centre. Identical charges of magnitude Q are placed at (n-1) corners. The field at the centre is

    A
    `k Q/(r^(2))`
    B
    `(n-1) k Q/(r^(2))`
    C
    `n/(n-1) kQ/(r^(2))`
    D
    `(n-1)/n k Q/(r^(2))`

  • In a regular polygon of n sides, each corner is at a distance r from the centre. Identical charges each of magnitude q are placed at corners. The field at the centre is

    A
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    B
    `(n-1)/(n)k(q)/(r^(2))`
    C
    0
    D
    `(n-1)k(q)/(r^(2))`