Question

A straight conductor of mass m and carrying a current i is hinged at one end and placed in a plane perpendicular to the magnetic field B as shown in figure. At any moment if the conductor is let free, then the angular acceleration of the conductor will be (neglect gravity)–

• A. $\frac { 3 \mathrm { iB } } { 2 \mathrm {~m} }$
• B.
• C.
• D. $\frac { 3 \mathrm { i } } { 2 \mathrm { mB } }$

Answer 1

Answer: (A)

$\frac { 3 \mathrm { iB } } { 2 \mathrm {~m} }$

Answer 2

Torque dt = dF × rb = iBdr × r t = $\int _ { 0 } ^ { \mathrm { L } } \mathrm { iBrdr } = \frac { \mathrm { iBL } { } ^ { 2 } } { 2 }$

a = $\frac { \tau } { \mathrm { I } }$ = $\frac { \mathrm { iBL } ^ { 2 } } { \frac { 2 \mathrm {~mL} ^ { 2 } } { 3 } }$ =