A uniform magnetic field exists in a square of side $$2a$$ (as$$ shown in $$figure). A square loop of side a enters the field along a diagonal and leave it at a constant speed. Draw the curve between induced emf e and distance along the diagonal, say xo.

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The graph is to be drawn qualitatively       As shown, for $$0$$ ≤ x ≤ aφ$$=Bx2$$ $$e=-d$$φ$$dt=-2B$$.$$dxdt=-2BxvAt$$  x $$=$$ $$0$$, e $$=$$ $$0At$$   x $$=$$ $$a/2$$, $$e=-BavAs$$, x→a but x≠a,e≈$$-2BavAs$$,  $$x=a$$, $$e=0$$ as φ$$=constantDistance$$ along diagonal When the loop reaches completely inside the field, it starts coming out of the field after some moment. When the loop is coming out, $$x1$$ should be selected carefully, for whichφ$$=Ba-x12e=-d$$φ$$dt=-2Ba-x1$$.$$v=2Ba-x1vAt$$  $$x1=0$$, e $$=2Bavx1=a$$, $$e=0Thus$$, before the loop enters the field completely, e $$=$$ $$-$$ $$2Bav$$. When the loop is completely inside the field, e $$=$$ $$0$$ $$($$φ $$=$$ $$constant)$$. As the loop starts coming out of the field (e$$ $$=$$ $$-2Bav). Option (4) is correct.

A uniform magnetic field exists in a square of side 2a (as shown in figure). A square loop of side a enters the field along a diagonal and leave it at a constant speed. Draw the curve between induced emf e and distance along the diagonal, say xo.

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