(a) Statement of Biot Savart law
Expression in vector form
Magnitude of magnetic field at centre
Direction of magnetic field
(a) It states that magnetic field strength,

→

dB

, due to a current element,

→

Idl

, at a point, having a position vector r relative to the current element, is found to depend (i) directly on the current element, (ii) inversely on the square of the distance |r| , (iii) directly on the sine of angle between the current element and the position vector r.

In vector notation,

→

dB

=‌

µ0

4π

‌

→ Idi × → r

| → r |3

(b) ‌Bπ=‌

µ0×1

2R

=‌

µ0

2R

(‌ along ‌z−‌ direction) ‌
‌BQ=‌

µ0×√3

2R

=‌

µ0√3

2R

‌ (along ‌x−‌ direction) ‌
‌∴B=√Bp2+BQ2=‌

µ0

R

This net magnetic field B, is inclined to the field Bp, at an angle θ, where
‌tan‌θ=√3
‌(θ=tan−1√3=60∘)
(in XZ plane)