Magnetic braking revisited

Abstract

The braking force acting on a conducting disk rotating under the influence of an external magnetic field of axial symmetry is calculated in a quasi-static approximation and the role played by the charge distributions induced in the disk is shown. The two cases of infinite and finite radius are considered to analyze the influence of edge effects and we obtain a general expression for the braking torque when the magnetic field has axial symmetry. The particular case of a uniform external magnetic field is used to show the working of a simplified model of a cylindrical battery. Analytical results are compared with those obtained by other authors. © 1997 American Association of Physics Teachers.

Analytical results for rotating and linear magnetic brakes

“…in agreement with the formula obtained by other authors [17,19,20]. From the condition dT nn /dc = 0 we can show that, for the case A >> a, the maximum value of T nn occurs at c =c withc…”

“…Plots of the field lines of J(ρ, φ) can be seen in Refs. [11,17,19]. Now we consider the presence of another magnetic pole with uniform magnetic field B 2 = B 2ẑ inside the circular region of radius a, with center at the distance c 2 located at (x = c 2 cos α, y = c 2 sin α).…”

“…Depending on the geometries of the conductor and the magnetic field, these space charges may be accompanied by an electric current density J, as in the case of the Faraday's first dynamo [9,10] and the induction motor [11]. References to these space charges on a magnetic brake made up of a disk rotating under the magnetic field of a single pole can be found in literature, [12,13,14,15,16,17] in the context of analytical calculations of forces and torques.…”

“…According to the convenience, only ρ F is calculated, ignoring the surface charge density σ F [17] or, conversely, only σ F is calculated ignoring the charge density ρ F [12,13,15,16]. The charge density at the external surface of the moving conductor (σ A ) is never mentioned in these works.…”

Design of a magnetic braking system

“…Experimental results are close to the theoretical predictions except near the disk edge [14]. The edge effects on the braking torque are further revealed by Aguirregabiria et al [15].…”