Question

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)

Answer 1

Correct Answer - B
`dvec(B)=(mu_(0)i)/(4pi) (dvec(l)xxvec(r))/(r^(3))`
(magnitude field at point `P`, at position `vec(r)`) magnetic field at origin due to current element at position `vec(r)`
`d vec(B)=-(mu_(0)i)/(4pi)((dvec(l)xxvec(r)))/(r^(3))=(mu_(0)i)/(4pi) (vec(r)xxdvec(l))/(r^(3))`