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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 dBcenter created by this ring at the center of the disk in terms of Q, R, w, dr, and other relevant constants. 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 re, 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 wat R D |гө FIG. 4: Arc length c) Sum up the contributions from all the rings by taking the integral Bcenter = f₁ 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 dBcenter created by this ring at the center of the disk in terms of Q, R, w, dr, and other relevant constants. 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 re, 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 wat R D |гө FIG. 4: Arc length c) Sum up the contributions from all the rings by taking the integral Bcenter = f₁ dBcenter (what are the limits of integration?). Answer: Bcenter = HoQw 2лR

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Hello, I really need help with part A, Part B and Part C I was wondering if you can help me with it and can you label which one is which thank you

 

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? b) Find the magnetic field dBcenter created by this ring at the center of the disk in terms of Q, R, w, dr, and other relevant constants. c) Sum up the contributions from all the rings by taking the integral Bcenter limits of integration?). Answer: Bcenter HoQw 2лR 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 re, 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 = dr = wat R 3 |гө FIG. 4: Arc length dBcenter (what are the
Transcribed Image Text: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? b) Find the magnetic field dBcenter created by this ring at the center of the disk in terms of Q, R, w, dr, and other relevant constants. c) Sum up the contributions from all the rings by taking the integral Bcenter limits of integration?). Answer: Bcenter HoQw 2лR 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 re, 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 = dr = wat R 3 |гө FIG. 4: Arc length dBcenter (what are the
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