{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

au10_312ps1_sol

au10_312ps1_sol - ECE312 Autumn 2010 Problem Set 1...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ECE312 Autumn 2010: Problem Set 1 Solutions Problem 1 : B = 5 μ ˆ y T, u = 3ˆ x + 4ˆ z m/s, m e = 9 . 1 × 10 − 31 kg, and q e =- 1 . 6 × 10 − 19 C. (a) The force on the electron: F = q u × B = (- 1 . 6 × 10 − 19 )(3ˆ x + 4ˆ z ) × 5 μ ˆ y = 5(- 1 . 6 × 10 − 19 )(4 π × 10 − 7 )(3ˆ z- 4ˆ x ) = (5 . 03 × 10 − 24 )(0 . 8ˆ x- . 6ˆ z ) N (b) The radius of the circular orbit: vextendsingle vextendsingle F vextendsingle vextendsingle = 5 . 03 × 10 − 24 = m | u | 2 r ⇒ r = (9 . 1 × 10 − 31 )(5) 2 (5 . 03 × 10 − 24 ) = 4 . 52 μ m (c) Given a circular orbit, the distance traveled in one orbit is 2 πr . Since the velocity | u | is 5 m/s, the time required to complete one orbit is 2 πr | u | = 5 . 68 μ s ⇒ f = (5 . 68 × 10 − 6 ) − 1 = 175 . 94 kHz This is called the “gyrofrequency” of the electron. Electrons circulating in these sorts of orbits are often used in devices for studying particle physics. Problem 2 : A coaxial cable with J = ˆ z (1+ r 2 ) flowing through a solid inner cylinder of radius 2 cm. The current returns on the outer shell of radius 5 cm. (a) Note this is a non-uniform current density, i.e. the current is less in the middle of the wire than on the outside following the function (1+ r 2 ). To use Ampere’s Law to find fields, we need a lot of symmetry. Here we have a cylindrical structure, so we choose a cylindrical coordinate system for this problem. In general the field would look like H ( r, φ, z ) = ˆ rH r ( r, φ, z ) + ˆ φH φ ( r, φ, z...
View Full Document

{[ snackBarMessage ]}

Page1 / 4

au10_312ps1_sol - ECE312 Autumn 2010 Problem Set 1...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon bookmark
Ask a homework question - tutors are online