A coaxial cable consists of an inner conducting cylinder of radius a and an outer conducting...

 

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A coaxial cable consists of an inner conducting cylinder of radius a and an outer conducting cylinder of radius 5a. A current / flows down the length of the inner cylinder and back along the length of the outer cylinder (that is, both cylinders carry current I, directed oppositely to one another). (a) Derive an expression for the self-inductance per unit length of this coaxial cable. (b) Derive an expression for the energy per unit length stored in this coaxial cable two ways: a. first, using the formula for the energy stored in an inductor, and b. second, but using the formula for the energy stored in a magnetic field. Show that your two results agree. (c) If I = 1.2 A, what is the energy stored in a 3 m length of the cable? A coaxial cable consists of an inner conducting cylinder of radius a and an outer conducting cylinder of radius 5a. A current / flows down the length of the inner cylinder and back along the length of the outer cylinder (that is, both cylinders carry current I, directed oppositely to one another). (a) Derive an expression for the self-inductance per unit length of this coaxial cable. (b) Derive an expression for the energy per unit length stored in this coaxial cable two ways: a. first, using the formula for the energy stored in an inductor, and b. second, but using the formula for the energy stored in a magnetic field. Show that your two results agree. (c) If I = 1.2 A, what is the energy stored in a 3 m length of the cable?

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a To derive an expression for the selfinductance per unit length of the coaxial cable we can use the ... View the full answer