Question

Biot-Savart Worksheet dB = Ho idỈxì 47 r3 1. Vector Product and the direction of dB di r Given a finite line of current as shown above does the direction of dĒ vary as dí is moved from one end to the other? Why? Assuming the page is the x-y plane and point p is on the page and not on the y axis. Suppose a line of current that is an arc that is a quarter of a circle oriented such the current at one end is traveling parallel to the y axis and at the other end is traveling parallel to the z axis. Does the direction of dB vary in this case? Why?

Answer 1

Let according to law, we have Biot-savast do lle idixr 47T de ig when No, there is no change in direction of do de moves from one end to other end. Because, according to given eqreation (1) direction of do depends on cross product (dixr). From this it is clear that direction of do is always perpendicular to the plane in which both de f g lies so here when de mores from one end to other end then there is no change in plane of both dear, hence de always remains perpendicular to plane of de f3. So its direction remains same while de moving from one end to other and

od -Y 8 p ak in this case, Yes, direction of to get vary because while moving from one end to other end de & h does not remains in same plane When te is at one end then de fy have particular plane but de moves from one end to other end then at every place the plane in conich te off lies changes contineously so according to our relation as is alway's perpendicular to the plane in which te &ð lies. So here plane of de 48 Changes contine ously hence direction of B also changes