Question

A wire ab of length l, mass m and resistance R slides on a smooth thick pair of metallic rails joined at the bottom as shown in fig. The plane of the rails makes an angle q with the horizontal. A vertical magnetic field B exist in the region. If the wire slides on the rails at a constant speed v, then the value of B is–

• A. $\sqrt { \frac { \mathrm { mgR } } { \mathrm { v } \ell ^ { 2 } \cos ^ { 2 } \theta } }$
• B. $\sqrt { \frac { \mathrm { mgR } \cos \theta } { \mathrm { v } \ell ^ { 2 } \sin ^ { 2 } \theta } }$
• C. $\sqrt { \frac { m g R } { v ^ { 2 } \ell ^ { 2 } \sin ^ { 2 } \theta } }$
• D. $\sqrt { \frac { \mathrm { mgR } \sin \theta } { \mathrm { v } \ell ^ { 2 } \cos ^ { 2 } \theta } }$

Answer 1

Answer: (A)

$\sqrt { \frac { \mathrm { mgR } } { \mathrm { v } \ell ^ { 2 } \cos ^ { 2 } \theta } }$

Answer 2

To find the magnetic field outside a thick conductor, the current may be assumed to flow along the axis. As points 1 , 2 , 3 are equidistant from the axis, B₁ = B₂ = B₃