Question

a current I is flowing in a conductor placed along the x axis as shown in the figure find the magnitude and direction of the magnetic field due to small current element dl lying at the origin at points (0,d,0) and 0,0,d

Answer 1

Given:

A current carrying conductor is placed along the x axis as shown in the diagram.

To find:

Magnitude and Direction of Magnetic Field Intensity at

• (0,0,d)

• (0,d,0)

Calculation:

1st case:

Applying Bio-Savart's Law :

$\therefore \: dB = \dfrac{ { \mu}_{0} }{4\pi} \times \bigg \{ \dfrac{I \times dl}{ {d}^{2} } \bigg \}$

Direction of magnetic field :

$\therefore \: d \vec{B} = \dfrac{ { \mu}_{0} }{4\pi} \times \bigg \{ \dfrac{I \times d \vec{l}}{ {d}^{2} } \bigg \} \: \hat{k}$

2nd case:

Applying Bio-Savart's Law:

$\therefore \: dB = \dfrac{ { \mu}_{0} }{4\pi} \times \bigg \{ \dfrac{I \times dl}{ {d}^{2} } \bigg \}$

Direction of magnetic field:

$\therefore \: d \vec{B} = \dfrac{ { \mu}_{0} }{4\pi} \times \bigg \{ \dfrac{I \times d \vec{l}}{ {d}^{2} } \bigg \} \: (- \hat{ j})$

Tricks to find out direction of magnetic field:

• Right Hand Thumb Rule

• Cross product between length vector and radial vector.