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The magnetic field at the origin due to ...

The magnetic field at the origin due to a current element I `(vec dl ) placed at a positon (vec r) is`

A

`(((mu_0 i)/(4pi))` `(vec (dl) xx vec (r))/r^3)`

B

`(-((mu_0)i/(4 pi) (vec(r) xx vec(dl) / r^3)))`

C

`((mu_0)i/(4 pi) (vec(r) xx vec(dl) / r^3))`

D

`(-((mu_0)i/(4pi)(vec (dl) xx vec (r))/r^3))`

Text Solution

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The correct Answer is:
C, D
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Knowledge Check

  • The magnetic field at the origin due to a current element I vec(dl) placed at position r is (i) ((mu_(0)i)/(4pi))((dvec(l)xxvec(r))/(r^(3))) -((mu_(0)i)/(4pi))((dvec(l)xxvec(r))/(r^(3))) (iii) ((mu_(0)i)/(4pi))((vec(r)xxdvec(l))/(r^(3))) -((mu_(0)i)/(4pi))((vec(r)xxdvec(l))/(r^(3)))

    A
    (i),(ii)
    B
    (ii),(iii)
    C
    (i),(ii)
    D
    (iii),(iv)

  • The magnetic field at the origin due to the current flowing in the wire is

    A
    `-(mu_0I)/(8pia)(hati+hatk)`
    B
    `(mu_0I)/(2pia)(hati+hatk)`
    C
    `(mu_0I)/(8pia)(-hati+hatk)`
    D
    `-(mu_0I)/(4piasqrt2) (hati-hatk)`

  • The magnetic field bar(dB) due to a small current element bar(dl) at a distance vec(r) and carrying current 'I' is

    A
    `bar(dB)=(mu_(0))/(4pi)i((bar(dl)xxbar(r))/(r))`
    B
    `bar(dB)=(mu_(0))/(4pi)i^(2)((bar(dl)xxbar(r))/(r^(2)))`
    C
    `bar(dB)=(mu_(0))/(4pi)i^(2)((bar(dl)xxbar(r))/(r))`
    D
    `bar(dB)=(mu_(0))/(4pi)i((bar(dl)xxbar(r))/(r^(3)))`

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