Question

3. (a) Use Biot-Savart Law to find the magnetic field of wire, along the z-axis, carrying a current I (in direction), at a point P a distance r from the wire. Do this for both a finite wire (21 <2<z2), and an infinite wire (-0<z< too). (6) Use the result of part (a) to evaluate the net magnetic field of the wires shown at point P (0,0,2). [15] z P (0,0,2) 22 di 0 B (0,2,0) tec у P(x,y) A (L,0,0) 11 X 21

Answer 1

Answer:- Biot-Savart Law: Biot-Savart's law is an equation that gives the magnetic field produced due to a current carrying segment. This segment is taken as a vector quantity as the current element - Currents which arise due to the motion of charges are the source of magnetic fields. When charges move in a conducting wire and produce a current I, the magnetic field at any point p due to the current can be calculated by adding up the magnetic field contributions, dë, from small segments of the wire ds. dB BI...P CS Scanned with CamScanner

These segments length can be thought of as a vector quantity having a magnitude of the of the segment and pointing in the direction of the current flow. The infinitesimal current source can then be written as I ds. Let & denote as the distance from the current source to the field point P, and Ộ the correspon- ding unit vector. The Biot- Savart law gives an expression for the magnetic field contribu- tion, dB. from the current source, Id}, dB = 4o I dix Idixi 34 47 where Ho is a constant called the bermeabi- lity of free space. Ho= 4A X10'T. MIA Notice that the expression is remarkably similar to the coulomb's law for the electric Field due to a charge element dq. CS Scanned with CamScanner

dE=/ 1 dq 4TG 82 cy Adding up these contributions to find the mag- netic field at the point p requires integrating over the the current source, BS dšy wire 47 22 wire S dix? dB= Ho I d8x 47 ४१ Ho I dx sino a 40 2² which shows that the magnetic field at p will point in the tŘ direction. CS Scanned with CamScanner

Biot-Savart’s law is an equation that gives the magnetic field produced due to a current carrying segment. This segment is taken as a vector quantity known as the current element.