InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
State Biot- Savart law. Use to obtain the magnetic field at a point due to a long, staright current carrying wire. |
|
Answer» Solution :For statement of Biot - Savart law, refer to point Number 6 under the heading "Chapter At A Glance". LET CD be a long, staright current carrying wire and P be a point situated at a normal distance R from the wire. Consider a current element `I vecdl` situated at a distance OA = I. If AP = r, then due to `DB = (mu_0)/(4pi) (I dl sin theta)/(r^2)` As PER figure `sin theta = sin (90^@ - phi) = cos theta` `:. I = R tan phi` `:. dl = R SEC^2 phi CDOT d phi` and `r = R sec phi` `:. dB = (mu_0)/(4pi)cdot ((R sec^2 phi_2.d phi)cos phi)/((R sec phi^2)) = (mu_0)/(4pi) cdot (I cos phi cdot d phi)/(R)` Therefore, the magnetic field due to whole wire CD will be `B = (mu_0 I)/(4 pi R) int_(-phi_1)^(phi_2) cos phi . d phi = (mu_0 I)/(4 pi R) [sin phi_2 - sin (-phi_1)] = (mu_0 I)/(4 pi R) [ sin phi_2 + sin phi_2]` Here `phi_2` has been taken +ve but `phi_1` has been taken -ve because it is in a direction opposite to that of `phi_2` For a long long wire (or infinitely long wire) `phi_1 = phi_2 = 90^@`, therefore `B = (mu_0 I)/(2 pi R)` 
|
|