Problem 3: A flat, circular disk of radius R is uniformly charged with to- tal charge Q. The disk spins at angular velocity @ about an axis through its center (see Fig.3). What is the magnetic field strength at the center of the disk? dr b) Find the magnetic field dB center created by this ring at the center of the disk in terms of Q, R, w, dr, and other relevant constants. wat R a) Choose a ring of width dr and radius r inside the disk, as shown in Fig.3. The amount of charge dq that passes through a cross-section of this ring in the interval of time dt is enclosed in the hatched section of this ring. Compute dq from the surface charge density of the disk and the area of the hatched region (note that the length of an arc of a circle with radius r is equal to r0, where is the angle in radians which the arc subtends at the center of the circle; see the scheme in Fig.4). Compute the current I flowing through this thin ring as dq/dt. FIG. 3: The scheme for Problem 3 3 |гө 2 FIG. 4: Arc length c) Sum up the contributions from all the rings by taking the integral Bcenter = ₁ dBcenter (what are the limits of integration?). Answer: Bcenter HoQw 2лR

Problem 3: A flat, circular disk of radius R is uniformly charged with to- tal charge Q. The disk spins at angular velocity @ about an axis through its center (see Fig.3). What is the magnetic field strength at the center of the disk? dr b) Find the magnetic field dB center created by this ring at the center of the disk in terms of Q, R, w, dr, and other relevant constants. wat R a) Choose a ring of width dr and radius r inside the disk, as shown in Fig.3. The amount of charge dq that passes through a cross-section of this ring in the interval of time dt is enclosed in the hatched section of this ring. Compute dq from the surface charge density of the disk and the area of the hatched region (note that the length of an arc of a circle with radius r is equal to r0, where is the angle in radians which the arc subtends at the center of the circle; see the scheme in Fig.4). Compute the current I flowing through this thin ring as dq/dt. FIG. 3: The scheme for Problem 3 3 |гө 2 FIG. 4: Arc length c) Sum up the contributions from all the rings by taking the integral Bcenter = ₁ dBcenter (what are the limits of integration?). Answer: Bcenter HoQw 2лR

Glencoe Physics: Principles and Problems, Student Edition

1st Edition

ISBN:9780078807213

Author:Paul W. Zitzewitz

Publisher:Paul W. Zitzewitz

Chapter24: Magnetic Fields

Section: Chapter Questions

Problem 103A

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