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PHY250H1 (2)
Midterm

# PHY250 2012 Midterm.pdf

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School
University of Toronto St. George
Department
Physics
Course
PHY250H1
Professor
Hae- Young Kee
Semester
Winter

Description
Midterm Test 250S, March 7, 2012 (Use notations in the textbook); Total 30 points Use Gauss’s law when it is appropriate (4 pt.) 1. Consider a function v = r r nˆ. (a) Compute the divergence of v. R R (b) Check the divergence theorem ( ∇ ▯ vdτ = v ▯ da) using a sphere of radius R. (6 pt) 2. Consider a ﬂat circular disk of radius R containing a circular hole in the middle (the circular hole is in the region 0 ≤ s < a where s is the radial distance), and it carries a uniform surface charge σ in the region a ≤ s ≤ R. (a) Find the electric ﬁeld a distance z above the center of the disk. (b) Check the limit z → ∞ (ﬁnd a ﬁrst ﬁnite term in a series expansion) Discuss the physical implication of your limiting case (hint; rewrite the electric ﬁeld in terms of total charge instead of σ). (6 pt) 3. Consider a hollow spherical shell that carries charge density ρ =
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