Question

A long thin wire carrying a current I1 =10 A (out of page) is located at (0, 0) and another wire carrying a current I2 =8A (into the page) is located at (x=9cm, y=0). Find the magnitude and direction of the magnetic field due to these two currents at (x=0, y=12 cm). Your solution must include a neat diagram

Answer 1

Given is:-

distance b/w I1 and (0,12) is 12 cm or 0.12m

distance b/w I2 and (0,12) is 15 cm or 0.15m (by using )

Now the magnetic field due to the infinetly long curren carrying wire at a point r distance away is given by

and direction is given by right hand rule.

Therefore

towards negative x axis

similarly

The diagram will be as shown below

Now the y component of B2 will be

and

Thus the y component of Net magnetic field is  

and

x component is

Net magnitude will be

and the direction is given by