A thin wire of mass m and length l has a resistance R. The wire can slide freely

Question

A thin wire of mass m and length l has a resistance R. The wire can slide freely, with no friction, along twin vertical rails (of negligible resistance) as shown below. A horizontal, uniform magnetic field of magnitude B is perpendicular to the rails and wire. Neglect the magnetic field of the Earth. The wire falls under the gravitational force near the surface of the Earth.

a. What is the terminal speed of the wire?

b. What is the direction of the current flowing in the wire?

c. Discuss the problem from the standpoint of energy considerations.

Explanation / Answer

a)

E = induced emf

i = induced current

R = Resistance

V = speed

induced emf is given as

E = BLV

induced current is given as

i = E/R = BLV/R

at equilibrium

weight = magnetic force

mg = i BL

mg = (BLV/R) BL

V = mgR / (B2L2)

b)

Using right hand rule , the direction of current is left to right

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.