A 2.5 m - long wire carries a current of 8.0 A and is immersed within a uniform magnetic field B⃗. When this wire lies along the + x axis, a magnetic force F⃗ = (-2.3j) N acts on the wire, and when it lies on the + y axis, the force is F⃗ = (2.3i-5.6k) N.

Part A - Find the x-component of B⃗.

Part B - Find the y-component of B⃗.

Part C - Find the z-component of B⃗.

Let the magnetic field be B = B₁i + B₂j + B₃k

Force = I (L x B), I is current, L is length and B is magnetic field.

In the first case

force = - 2.3 j N

L = 2.5 i

puting the values in the equation above

- 2.3 j = 8 [ 2.5 i x (B₁i + B₂j + B₃k) ]

= - 20 B₃ j + 20 B₂ k

comparing LHS and RHS,

20B₃ = 2.3

B₃ =.115

B₂ = 0

In the second case

L = 2.5 j

Force = I (L x B)

2.3i-5.6k = 8 (2.5 j x (B₁i + B₂j + B₃k)

= - 20 B₁ k + 20B₃ i

2.3i-5.6k = - 20 B₁ k + 20B₃ i

B₃ =.115

B₁ =.28

So magnetic field B =.28 i +.115 B₃

Part A

x component of B =.28 T

Part B

y component of B = 0

Part C

z component of B =.115 T.