# ps08 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of...

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Problem 1: In this problem you will work through two examples from Problem Solving 7: Ampere’s Law. OBJECTIVES 1. To learn how to use Ampere’s Law for calculating magnetic fields from symmetric current distributions 2. To find an expression for the magnetic field of a cylindrical current-carrying shell of inner radius a and outer radius b using Ampere’s Law. 3. To find an expression for the magnetic field of a slab of current using Ampere’s Law. REFERENCE: Section 9-3, 8.02 Course Notes . Summary: Strategy for Applying Ampere’s Law (Section 9.10.2, 8.02 Course Notes) Ampere’s law states that the line integral of d Bs r r around any closed loop is proportional to the total steady current passing through any surface that is bounded by the closed loop: 0e n c dI μ ⋅= r r ± To apply Ampere’s law to calculate the magnetic field, we use the following procedure: Step 1: Identify the ‘symmetry’ properties of the current distribution. Step 2: Determine the direction of the magnetic field Step 3: Decide how many different spatial regions the current distribution determines For each region of space… Step 4: Choose an Amperian loop along each part of which the magnetic field is either constant or zero Step 5: Calculate the current through the Amperian Loop Step 6: Calculate the line integral d r r ± around the closed loop. Step 7: Equate d r r ± with n c I and solve for B r .
Example 1: Magnetic Field of a Cylindrical Shell We now apply this strategy to the following problem. Consider the cylindrical conductor with a hollow center and copper walls of thickness b a as shown . The radii of the inner and outer walls are a and b respectively, and the current I is uniformly spread over the cross section of the copper (shaded region). We want to calculate the magnetic field in the region a < r < b .

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ps08 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of...

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