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Unformatted text preview: Kapoor (mk9499) – homework22 – Turner – (60230) 1 This print-out should have 11 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 3) 10.0 points An infinite sheet lying in yz plane is carrying a current which is uniform along the y direction, as illustrated below. The current is flowing along the negative z direction. The permeability of free space is 1 . 25664 × 10 − 6 N / A 2 . b a x y A C D F E z What is the direction of magnetic field vector B at point A, which is located on the negative x-axis ( i.e. , x < 0)? Caution: See the sketch to confirm the location of the point A. 1. hatwide B = ( ˆ i − ˆ j ) √ 2 2. hatwide B = − ( ˆ i − ˆ j ) √ 2 3. hatwide B = ( ˆ i + ˆ j ) √ 2 4. hatwide B = − ˆ k 5. hatwide B = − ˆ ı 6. hatwide B = − ˆ 7. hatwide B = ˆ correct 8. hatwide B = − ( ˆ i + ˆ j ) √ 2 9. hatwide B = ˆ ı 10. hatwide B = ˆ k Explanation: Basic Concepts: Right-hand rule for de- termining the direction of vector B . Amp´ ere’s Law: contintegraldisplay vector B · vector ds = μ I . Solution: Consider that the current sheet consists of infinite number of current wires connected in parallel. We can easily deter- mine the direction of vector B for one wire with right-hand rule. Then the direction of vector B for two wires set together in parallel can be found (as illustrated below) by superposition prin- ciple. By symmetry, the direction of vector B due to an infinite current sheet is therefore along positive y direction (ˆ ) in the part of space where x < 0. 002 (part 2 of 3) 10.0 points Ampere’s Law states that contintegraldisplay vector B · dvectors = μ I Denote the magnetic field at A by B A . Eval- uate the loop integral along the rectangular loop CDEFC , where EF = a and FC = b . The magnitude of this loop integral is given by 1. contintegraldisplay vector B · dvectors = a + b 2 B A . 2. contintegraldisplay vector B · dvectors = b − a 2 B A . 3. contintegraldisplay vector B · dvectors = radicalbig a 2 + b 2 B A . 4. contintegraldisplay vector B · dvectors = 2 a B A ....
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