Answer:
E: None of the above
Explanation:
Since the force on the wire F = ∫idL × B where i = current in wire = 2.0 mA = 2.0 × 10⁻³ A, dL = vector length of wire = dyj and we integrate from y₁ = 0 m and y₂ = 0.25 m, and B = magnetic field = (0.3y)i + (0.4y)j
So, F = ∫idL × B
and we integrate from y₁ = 0 m and y₂ = 0.25 m
F = 2.0 × 10⁻³ A∫₀⁰°²⁵[dyj m × (0.3y)i + (0.4y)j]
F = 2.0 × 10⁻³ A∫₀⁰°²⁵[dyj m × (0.3y)i + dyj m × (0.4y)j]
F = 2.0 × 10⁻³ A∫₀⁰°²⁵[(0.3y) × dy(j × i) + 0.25 × (0.4y)(j × j)]
F = 2.0 × 10⁻³ A∫₀⁰°²°⁵[(0.3ydy(-k) + 0.1y)(0)]
F = 2.0 × 10⁻³ A∫₀⁰°²⁵(-0.3ydy)k
F = 2.0 × 10⁻³ A[-0.3y²/2]₀⁰°²⁵k
F = -2.0 × 10⁻³ A[0.3(0.25)²/2 - 0.3(0)²/2]k
F = -2.0 × 10⁻³ A[0.3(0.0625)/2 - 0]k
F = -2.0 × 10⁻³ A[0.3(0.0625)/2]k
F = -1 × 10⁻³[0.01875]k N
F = -[0.01875 × 10⁻³]k N
F = -[1.875 × 10⁻⁵]k N
Since the answer is not contained in the options, the answer is E.
