On a smooth plane inclined at 30 degree with the horizontal , a thin current – carrying metallic rod is placed parallel to the horizontal ground. The plane is located in a uniform magnetic field of 0.15 T in the vertical direction.For what value of current can the rod remain stationary? The mass per unit length of the rod is 0.03 kg / m.Ans:11.32.Explain with diagram plz.

On a smooth plane inclined  at  30 degree with  the  horizontal ,  a thin  current – carrying metallic rod is placed  parallel  to the  horizontal ground. The plane is located in a uniform magnetic field of 0.15 T in  the  vertical  direction.For what value of current can the rod remain stationary? The mass per unit length of the rod is 0.03 kg / m.Ans:11.32.Explain with diagram plz.


1 Answers

25757 Points
4 years ago
the current carrying rod will remain stationary when net vector summation  all  forces acting on the body is  zero
hence the force due to magnetic field  acting on current carrying rod is Bil in horizontal direction 
now taking the component of magnetic force along the plane (up)
F upward = Bi L cos 30 = BiL * sqrt (3) / 2
F downward the gravity = mg sin 30 = mg/2
for equilibrium
F upward   = F downward
i = mg / BL * sqrt (3)
i = 0.03 * 10 / 0.15 * 1 * 1.732
i = 1.15 Amp

Think You Can Provide A Better Answer ?