Concepts Of Physics MCQ Edition [Volume 2]PhysicsMagnetic Field due to a Current
As illustrated in the figure, two parallel wires separated by a distance of 4.0 cm carry equal currents of 10 A in opposite directions. Determine the magnitude of the magnetic field B at points A₁ , A₂ , A₃ , and A₄ respectively.
Options
- A1.33 10⁻⁴ T , 1.33 10⁻⁴ T , 0 T , 1.41 10⁻⁴ T
- B0.33 10⁻⁴ T , 1.35 10⁻⁴ T , 1.0 10⁻⁴ T , 0.5 10⁻⁴ T
- C1.33 10⁻⁴ T , 5.4 10⁻⁴ T , 4.0 10⁻⁴ T , 2.0 10⁻⁴ T
- D0.67 10⁻⁴ T , 2.7 10⁻⁴ T , 2.0 10⁻⁴ T , 1.0 10⁻⁴ T
Correct answer
D. 0.67 10⁻⁴ T , 2.7 10⁻⁴ T , 2.0 10⁻⁴ T , 1.0 10⁻⁴ T
Step-by-step solution
The magnetic field due to a long straight wire carrying current I at a distance r is given by B = ₀ I 2 r . Given I = 10 A , the constant ₀ I 2 = 4 10⁻⁷ 10 2 = 2 10⁻⁶ T m . Let the left wire be W₁ (current into the page) and the right wire be W₂ (current out of the page). The distance between them is 4 cm . For point A₁ : Distance from W₁ is r₁ = 2 cm = 0.02 m . Distance from W₂ is r₂ = 2 + 4 = 6 cm = 0.06 m . Since A₁ is outside the wires and the currents are in opposite directions, the magnetic fields oppose each