Question

A rigid circular loop of radius r and mass m lies in the x-y plane of a flat table and has a current flowing in it. At this particular place the earth's magnetic field is = B_x + B_z. The value of i so that the loop start tilting is-

• A.
• B. $\frac { \mathrm { mg } } { \pi \mathrm { rB } }$
• C.
• D. $\frac { \mathrm { mg } } { \pi \mathrm { r } \sqrt { \mathrm { B } _ { \mathrm { x } } \mathrm { B } _ { \mathrm { z } } } }$

Answer 1

Answer: (B)

$\frac { \mathrm { mg } } { \pi \mathrm { rB } }$

Answer 2

$\overrightarrow { \mathrm { M } }$ = i(πr²), $\vec { B }$ = B_x i + B_z

for start tilting τ_{due to mass}

= τ_magnetic $| ( \mathrm { mg } ) \mathrm { r } |$ = $| \overrightarrow { \mathrm { M } } \times \overrightarrow { \mathrm { B } } |$ (mg) (r) = i(πr²)(B_x) i =