A square coil of edge I having n turns carries a current i . It is kept on a smooth horizontal plate. A uniform magnetic field B exists in a direction parallel to an edge. The total mass of the coil is m . The minimum value of B for which the coil will start tipping over

Question

A square coil of edge I having n turns carries a current i . It is kept on a smooth horizontal plate. A uniform magnetic field B exists in a direction parallel to an edge. The total mass of the coil is m . The minimum value of B for which the coil will start tipping over (A) ((m g/n i l))2 (B) (2 m g/n i l) (C) (m g/2 n i l) (D) (m g/n i l) '

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-1cx6z10qt9li.png" /> Deflecting torque =niâABsin90 =nil2B Restoring torque =mg(l/2) For tipping nil2B≥ (m g l/2) ⇒ B≥ (m g/2 n i l) ∴ Bm i n=(m g/2 n i l)

Q. A square coil of edge $I$ having n turns carries a current $i$ . It is kept on a smooth horizontal plate. A uniform magnetic field $B$ exists in a direction parallel to an edge. The total mass of the coil is $m$ . The minimum value of $B$ for which the coil will start tipping over

$(\frac{m g}{ni l})^{2}$

$\frac{2 m g}{ni l}$

$\frac{m g}{2 ni l}$

$\frac{m g}{ni l}$ '

Deflecting torque $= ni A B s in 90$
$= ni l^{2} B$
Restoring torque $= m g \frac{l}{2}$
For tipping $ni l^{2} B \geq \frac{m g l}{2}$
$\Rightarrow B \geq \frac{m g}{2 ni l}$
$∴ B_{min} = \frac{m g}{2 ni l}$

Q. A square coil of edge I having n turns carries a current i . It is kept on a smooth horizontal plate. A uniform magnetic field B exists in a direction parallel to an edge. The total mass of the coil is m . The minimum value of B for which the coil will start tipping over

(nilmg​)2

nil2mg​

2nilmg​

nilmg​ '