A rectangular loop of sides 12 cm and 5 cm, with its sides parallel to the x-axis and y-axis, moves with a velocity of 5 cm/s along +x, in a space containing a variable magnetic field along +z. The field has a gradient of 10⁻³ T/cm along −x and it is decreasing with time at 10⁻³ T/s. If the resista…

Question

A rectangular loop of sides 12 cm and 5 cm, with its sides parallel to the x-axis and y-axis, moves with a velocity of 5 cm/s along +x, in a space containing a variable magnetic field along +z. The field has a gradient of 10⁻³ T/cm along −x and it is decreasing with time at 10⁻³ T/s. If the resistance of the loop is 6 mΩ, the power dissipated as heat is × 10⁻⁹ W.

Accepted Answer

216. Two things change the flux at once, so add both emfs. Motion through the gradient: ε₁=Av(dB)/(dx)=6×10⁻³×0.05×0.1=3×10⁻⁵ V. Field dying with time: ε₂=A(dB)/(dt)=6×10⁻³×10⁻³=6×10⁻⁶ V. ε=3.6×10⁻⁵ V, so P=(ε²)/R=((3.6×10⁻⁵)²)/(6×10⁻³)=216×10⁻⁹ W.

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