P30_025.PDF

has length √ 2 a ,so r = a/ √ 2and B = µ 0 i/ √ 2 πa . The ﬁelds due to the wires at the upper left and lower

right corners both point toward the upper right corner of the square. The ﬁelds due to the wires at the

upper right and lower left corners both point toward the upper left corner. The horizontal components

cancel and the vertical components sum to

B total =4 µ 0 i

√ 2 πa cos45 ◦ = 2 µ 0 i

πa

2(4 π

m / A)(20A)

π (0 . 20m)

=8 . 0

10 − 5 T .

In the calculation cos45 ◦ was replaced with 1 / √ 2. The total ﬁeld points upward.

25. Each wire produces a ﬁeld with magnitude given by B = µ 0 i/ 2 πr ,where r is the distance from the

corner of the square to the c enter. Accordin g to the Pythagorean theorem, the diagonal of the square

10 − 7 T