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Phys351-Assignment6-2009

# Phys351-Assignment6-2009 - potential functions that can be...

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Assignment #5, Due Thursday, Mar. 12th by 10:00 AM. 1. Two charges Q 1 and Q 2 are placed at points ( x = 0 , y = 0 , z = d 1 ) and ( x = 0 , y = 0 , z = - d 2 ) respectively. In their vicinity there is a grounded sphere of radius R < d 1 d 2 . Draw a diagram showing all relevant information of this problem and determine potential at the point point ( r = d 2 , θ = π/ 2 , φ ). 2. A very long pipe of rectangular cross section (of dimensions a and b ) is placed along the z-axis. The potential on all surfaces (i.e., x=0, y=0, y=b) except on x = a is zero. The potential on the surface x = a is given by V 0 sin 3 πy b · . Find the potential at every point inside the pipe. 3. The charge density on a sphere of radius R is given by σ 0 sin 2 θ
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Unformatted text preview: potential functions that can be used to determine potential at any point inside or outside the sphere. 4. The potential on a very long (assume inﬁnite) cylinder of radius R is given by V sin(3 φ ). The z-axis lies along the axis of the cylinder. Determine potential inside and outside the cylinder. 5. The potential on a very long (assume inﬁnite) cylinder of radius R is given by V cos 3 φ . The z-axis lies along the axis of the cylinder. Determine potential inside and outside the cylinder. Hint: cos 3 φ = 1 2 cos φ (cos2 φ + 1) = h 1 2 cos φ + 1 4 cos φ-cos3 φ i...
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