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Emf in a loop moving through a field that varies with position

This type of question, asked 2 times: 2021 Paper 6, 1 Feb 2024. All 2 questions below, oldest first.

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  1. Question 1

    2021 Paper 6

    17
    The magnetic field in a region is given by B→=B0(xa)k^\overrightarrow{B}=B_{0}\left( \frac{x}{a} \right)\widehat{k}. A square loop of side dd is placed with its edges along the xx and yy axes. The loop is moved with a constant velocity v→=v0i^\overrightarrow{v}=v_{0}\widehat{i}. The emf induced in the loop is:

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  2. Question 2

    1 Feb 2024

    22
    A rectangular loop of sides 12 cm12\text{ }cm and 5 cm5\text{ }cm, with its sides parallel to the xx-axis and yy-axis respectively moves with a velocity of 5 cm/s5\text{ }cm/s in the positive xx axis direction, in a space containing a variable magnetic field in the positive zz direction. The field has a gradient of 10−3 T/cm10^{- 3}\text{ }T/cm along the negative xx direction and it is decreasing with time at the rate of 10−3 T/s10^{- 3}\text{ }T/s. If the resistance of the loop is 6 mΩ6\text{ }m\Omega, the power dissipated by the loop as heat is ______ ×10−9 W\times10^{- 9}\text{ }W.