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HW1SP12 - cylindrical coordinates(a Calculate the total...

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Physics 4322 Homework Set 1 January 17, 2012 Due: Tuesday, January 24, 2012 1. Evaluate (3 x ^ - 2 y ^ ) · [( x ^ - y ^ - z ^ ) × ( x ^ + 3 z ^ )]. 2. Calculate the divergence and curl of the vector A = x 2 x ^ – xy 3 y ^ + 3z z ^ . 3. A dielectric rod having length L carries a linear charge density given by λ ( y' ) = o (2/ L ) y' as shown. (a) Calculate the electric potential along the x axis. (b) Calculate the electric field along the x axis. (c) Is it possible to calculate the electric field from the electric potential using the results from (a)? Explain. 4. Three infinite planes carrying surface charge densities + σ , - , and +2 are located at x = - a , x = 0, and x = + a , respectively, as shown. Calculate the electric field at all points along the x axis. 5. A wire having radius R carries a current whose current density J is given by J = J o ( s' / R ) (1/2) z ^ , where s' is the radial component in
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Unformatted text preview: cylindrical coordinates. (a) Calculate the total current I . (b) Calculate the magnetic field B inside and outside the wire. 6. An electric field E is given by E = E o [( x / a ) 2 x ^ + ( y / b ) 3 y ^ ], where a and b are constants. (a) Calculate the charge density that produced it. (b) Calculate the potential difference between the origin and the point x = 3 a . 7. A magnetic field B is given by B = B o [( y / a ) 2 x ^ + ( x / b ) y ^ ], where a and b are constants. (a) Calculate the current density that produced it. (b) Are there any restrictions on the values for a and b in order that div B = 0? 8. Outline the method for solving Laplace’s equation in two dimensions in right-handed, rectangular, Cartesian coordinate systems. y x z out x x=-a x=0 x=+a...
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