A conducting square loop is placed in a magnetic field B with its plane perpendicular to the field. The sides of the loop start shrinking at a constant rate α/. The induced emf in the loop at an instant when its side is ‘a’ is

Question

A conducting square loop is placed in a magnetic field B with its plane perpendicular to the field. The sides of the loop start shrinking at a constant rate α/. The induced emf in the loop at an instant when its side is ‘a’ is (A) 2aα β (B) a2 α β (C) 2a2α β (D) aα β

Tardigrade Admin · Accepted Answer

At any time t, the side of the square a=(a0-α t), where a0= side at t=0. At this instant, flux through the square: φ= BA cos 0°= B ( a 0-α t )2 ∴ emf induced E =-( d φ/ dt ) ⇒ E =- B ⋅ 2( a 0-α t )(0-α)=+2 α a β

Q. A conducting square loop is placed in a magnetic field $B$ with its plane perpendicular to the field. The sides of the loop start shrinking at a constant rate $α /$ . The induced emf in the loop at an instant when its side is ‘ $a$ ’ is

$2 a α β$

$a^{2} α β$

$2 a^{2} α β$

$a α β$

At any time $t$ , the side of the square $a = (a_{0} - α t)$ ,
where $a_{0} =$ side at $t = 0$ .
At this instant, flux through the square:
$ϕ = B A cos 0^{\circ} = B (a_{0} - α t)^{2}$
$∴$ emf induced $E = - \frac{d ϕ}{d t}$
$\Rightarrow E = - B \cdot 2 (a_{0} - α t) (0 - α) = + 2 α a β$

Q. A conducting square loop is placed in a magnetic field B with its plane perpendicular to the field. The sides of the loop start shrinking at a constant rate α/. The induced emf in the loop at an instant when its side is ‘a’ is

2aαβ

a2αβ

2a2αβ

aαβ