Barlow's wheel (Fig.) is a simple motor, whose construction is similar to Faraday's disk, but its operation is opposite. From a source of electromotive voltage U e = 3.00 V , electric curr

Question

Barlow's wheel (Fig.) is a simple motor, whose construction is similar to Faraday's disk, but its operation is opposite. From a source of electromotive voltage $U_{e} = 3.00 V$ , electric current is supplied to the metallic disk via a sliding contact $K_{1}$ , which touches the axis of the disk, and a liquid contact $K_{2}$ , made using a container of mercury, which touches the lower edge of the disk. The circuit resistance can be regulated using a rheostat in the range of $R_{1} = 3.00Ω$ to $R_{2} = 6.00Ω$ . The lower edge of the disk, together with contact $K_{2}$ , is located in a transverse magnetic field between the poles of the magnet. For simplicity, assume that the magnetic induction is constant across the entire area of the disk and has a value of $B = 800 mT$ . The magnetic field will cause the disk to rotate. The disk has a radius $r_{0} = 120 mm$ and the moment of inertia about its axis is $J = 5.00 \times 1 0^{- 4} kg . m^{2}$ . Mechanical resistance is not considered.

TestHub · Accepted Answer

A radial disk current experiences magnetic torque:

$τ = \frac{I B r _{0}^{2}}{2}$

Rotation produces a back emf:

$E_{b} = \frac{B ω r _{0}^{2}}{2}$

$I = \frac{U _{e} - E _{b}}{R}$

(A) The shown current and field give clockwise rotation from the stated view: false.

(B) At the maximum speed, current tends to zero.

$ω_{m a x} = \frac{2 U _{e}}{B r _{0}^{2}}$

It does not depend on R: true.

(C) Initially the back emf is zero.

$α = \frac{U _{e} B r _{0}^{2}}{2 R J}$

$α = \frac{3 ( 0.8 ) ( 0.0144 )}{2 ( 3 ) ( 5 \times 1 0 ^{- 4} )}$

$α = 11.52 rad/ s^{2}$

(C) is true.

(D) Doubling R halves the initial acceleration.

$α = 5.76 rad/ s^{2}$

(D) is true. Answer: B, C, D.

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