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Answer

0.065 A0.065 \text{ A}

Step-by-step solution

4 steps
  1. Identify the given values and the condition for suspension.

    The wire is suspended, meaning the upward magnetic force (FBF_B) must balance the downward gravitational force (FgF_g).
    Given:
    Length of wire, L=15 mL = 15 \text{ m}
    Mass of wire, m=50 g=0.050 kgm = 50 \text{ g} = 0.050 \text{ kg} (converted to kilograms)
    Magnetic field strength, B=0.50 TB = 0.50 \text{ T}
    Angle between wire and magnetic field, θ=90∘\theta = 90^\circ (since it's at a right angle)
    Acceleration due to gravity, g=9.8 m/s2g = 9.8 \text{ m/s}^2

  2. Write the formulas for magnetic force and gravitational force.

    The magnetic force on a current-carrying wire is given by:

    FB=BILsin⁡θF_B = BIL \sin\theta

    The gravitational force (weight) of the wire is given by:

    Fg=mgF_g = mg
  3. Equate the forces and solve for the current (II).

    For the wire to be suspended, FB=FgF_B = F_g:

    BILsin⁡θ=mgBIL \sin\theta = mg

    Rearrange the formula to solve for II:

    I=mgBLsin⁡θI = \frac{mg}{BL \sin\theta}
  4. Substitute the values and calculate the current.

    Since θ=90∘\theta = 90^\circ, sin⁡θ=sin⁡(90∘)=1\sin\theta = \sin(90^\circ) = 1.

    I=(0.050 kg)(9.8 m/s2)(0.50 T)(15 m)(1)I = \frac{(0.050 \text{ kg})(9.8 \text{ m/s}^2)}{(0.50 \text{ T})(15 \text{ m})(1)} I=0.49 N7.5 T⋅mI = \frac{0.49 \text{ N}}{7.5 \text{ T} \cdot \text{m}} I=0.065333... AI = 0.065333... \text{ A}

    Rounding to two significant figures, based on the given values (0.50 T, 50 g):

    I=0.065 AI = \boxed{0.065 \text{ A}}
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