Very simple combining fields question

[Jacob87411]

Our book never says how to combine two magnetic fields so can someone just tell me how it works.

Say we have a 1.2 x 10^-5 T going down and the Earth's field 5.0 x 10^-5 T going right. Whats the field created by the two.

 

[HallsofIvy]

Magnetic fields are vectors. that's why you are told both "1.2 x 10^-5" and "going down". They add like vectors.

You can represent this as a right triangle with legs of length 1.2 x 10^-5 (downward) and 5.0 x 10-5 (rightward). The sum of the two vectors is represented by the hypotenuse of that triangle. You can find the length by the Pythagorean theorem and the angle by using the arctan.

 

[Jacob87411]

Ah so the magnitude of the field will be the hypotenuse and the direction is from the arctan