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AB and CD are long staright conductors, ...

`AB` and `CD` are long staright conductors, distance `d` apart, carrying a current `I`. The magnetic field on `BC` due to the currents in `AB` and `CD`

A

is zero at all points

B

is zero at this midpoint

C

has different magnitudes at different points

D

is maximum at its midpoints

Text Solution

Verified by Experts

The correct Answer is:
C

Magnetic field at `P`,
Due to `①, B_(1)=(mu_(0)I)/(4pix), ox`
Due to `②, B_(2)=(mu_(0)I)/(4pi(d-x)), ox`
`B_(P)=B_(1)+B_(2)=(mu_(0)I)/(4pi)[1/x+1/(d-x)]`
`=(mu_(0)I)/(4pi).d/(x(d-x)), ox`
`x(d-x)` is maximum if
`x=d-x` i.e, `x=d//2`
At `x=d/2` (mid-point of `BC`), magnetic field is minimum.
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Knowledge Check

  • AB and CD are long straight conductor, distance d apart, carrying a current I . The magnetic field at the midpoint of BC is

    A
    `(-mu_(0)I)/(2pid)hatk`
    B
    `(-mu_(0)I)/(pid)hatk`
    C
    `(-mu_(0)I)/(4pid)hatk`
    D
    `(-mu_(0)I)/(8pid)hatk`

  • AB and CD are long straight conductor, distance d apart, carrying a current l. The magnetic field at the midpoint of BC is

    A
    `(-mu_(0)I)/(2pid)hatk`
    B
    `(-mu_(0)I)/(pid)hat k`
    C
    `(-mu_(0)I)/(4pid)hat k`
    D
    `(-mu_(0)I)/(8pid)hat k`

  • Shown in the figure is a conductor carrying a current i. the magnetic field at the origin is :

    A
    `(mu_(0) i)/(4r) ((hat(i))/(pi) + (hat(j))/(2))`
    B
    `- (mu_(0) i)/(4r) ((hat(i))/(pi) + (hat(k))/(2))`
    C
    `(mu_(0) i)/(4 r) ((hat(i))/(2) + (hat(i))/(pi))`
    D
    `(mu_(0) i)/(4r) ((2hat(i))/(pi) + hat(j))`

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