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The charge per unit length of the four q...

The charge per unit length of the four quadrant of the ring is `2 lambda, -2lambda, lambda` and `-lambda` respectively. The electric field at the centre is:

A

`(-lambda)/(2piepsilon_(0)R)hat(i)`

B

`lambda/(2pi epsilon_(0)R) hat(j)`

C

`(sqrt(2)lambda)/(4 pi epsilon_(0)R) hat(i)`

D

None

Text Solution

Verified by Experts

The correct Answer is:
A

`E_("net")=sqrt(2)E=sqrt(2)[(lambdasqrt(2))/(4pi in_(0)R)]rArr vec(E)=(lambda(-hat(i)))/(2pi in_(0)R)`
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Knowledge Check

  • The linear charge density on upper half of semi-circular section of ring is lambda and that at lower half is -lambda . The direction of electric field at centre O of ring is :

    A
    along OA
    B
    along OB
    C
    along OC
    D
    along OD
  • A charged wire is bent in the form of a semicircular arc of radius a. If charge per unit length is lambda coulomb/metre, the electric field at the centre O is

    A
    `(lambda)/(2pi a^(2)epsilon_(0))`
    B
    `(lambda)/(4pi^(2)epsilon_(0)a)`
    C
    `(lambda)/(2pi epsilon_(0)a)`
    D
    zero
  • A half ring of radius R has a charge of lambda per unit length. The electric force on 1C charged placed at the center is

    A
    zero
    B
    `(klambda)/R`
    C
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    D
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