Two mutually perpendicular

PHYSICS · Multi-part · CBSE · Physics · Magnetic Effects of Electric Current · Magnetic Effects of Electric Current

Problem

Two mutually perpendicular, long, straight wires intersect at the origin but are electrically insulated from each other. One wire lies along the

x

-axis and carries a current of

5.0\,\text{A}

in the

+x

direction; the other lies along the

y

-axis and carries a current of

3.0\,\text{A}

in the

+y

direction. Consider points that lie on the line

y = x

in the first quadrant. Let a generic point on this line be

S(s, s)

, where

s > 0

. (a) Express the magnetic-field vector produced at

S

by each wire in component form. (b) Derive expressions for the

x

- and

y

-components of the net magnetic field at

S

as functions of

s

. (c) Determine the value of

s

for which the net magnetic field at

S

is directed purely perpendicular to the plane (i.e., has no component parallel to either axis). (d) Discuss qualitatively whether such a value of

s

would exist if the direction of the current in the

y

-axis wire were reversed while the

x

-axis current remained unchanged.