Concepts Of Physics MCQ Edition [Volume 2]PhysicsElectromagnetic Induction
A wire ab of length l , mass m , and resistance R slides on a smooth, thick pair of metallic rails connected at the bottom, as shown in the figure. The plane of the rails forms an angle heta with the horizontal. A vertically directed magnetic field B exists in the region. If the wire slides on the rails at a constant speed v , determine the magnetic field B .
Options
- Am g R v l^2 ^2
- Bm g R v l^2 ^2
- Cm g R ^2 v l^2
- Dm g R v l^2 ^2
Correct answer
A. m g R v l^2 ^2
Step-by-step solution
The wire moves down the inclined plane with a constant speed v . The horizontal component of its velocity, which is perpendicular to the vertically directed magnetic field B , is v . The motional EMF induced in the wire is given by: E = B l (v ) The induced current I in the circuit is: I = E R = B l v R The magnetic force acting on the current-carrying wire is horizontal and its magnitude is: F_m = I l B The component of this magnetic force along the inclined plane opposes the downward motion and is given by: F_ up