Question

Four long, straight wires, each carrying a current of 5.0A, are placed in a plane as shown in figure (35-E3). The points of intersection form a square of side 5.0cm. (a) Find the magnetic field at the centre P of the square. (b) Q₁, Q₂, Q₃ and Q₄ are points situated on the diagonals of the square and at a distance from P that is equal to the length of the diagonal of the square. Find the magnetic fields at these points.

Answer 1

(a) For each of the wire

Magnitude of magnetic field

For AB ⊙ for BC⊙ For CD ⊗ and for DA ⊗.

The two ⊙ and 2⊗ fields cancel each other. Thus B_net = 0

(b) At point Q₁

due to (1)B

= 4 × 10^–5⊙

due to (2)B

= (4/3) × 10^–5⊙

due to (3)B

= (4/3) × 10^–5⊙

due to (4) B =

= 4 × 10^–5⊙

B_net = [4 + 4 + (4/3) + (4/3)] × 10^–5 = 32/3 × 10^–5 = 10.6 × 10^–5 ≈ 1.1 × 10^–4T

At point Q₂

At point Q₃

B_net = [4 + 4 + (4/3) + (4/3)] × 10^–5 = 32/3 × 10^–5 = 10.6 × 10^–5 ≈ 1.1 × 10^–4T