28. Sources of Magnetic Field

28. Sources of Magnetic Field - Problem View Magnetic Field...

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[ Problem View ] Magnetic Field near a Moving Charge Description: Use Biot-Savart law to find the magnetic field at various points due to a charge moving along the z axis. A particle with positive charge is moving with speed along the z axis toward positive . At the time of this problem it is located at the origin, . Your task is to find the magnetic field at various locations in the three-dimensional space around the moving charge. Part A Which of the following expressions gives the magnetic field at the point due to the moving charge? A. B. C. D. ANSWER: A only B only C only D only both A and B both C and D both A and C both B and D The main point here is that the r -dependence is really . The results from using
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in the numerator rather than the unit vector . A second point is that the order of the cross product must be such that the right-hand rule works: If your right thumb is along the direction of the current, , your fingers must curl along the direction of the magnetic field. Part B Find the magnetic field at the point . Part B.1 Part not displayed Express your answer in terms of , , , and , and use , , and for the three unit vectors. ANSWER: = (mu_0/(4*pi))*(q*v/x_1^2)*y_unit Part C Find the magnetic field at the point . Express your answer in terms of , , , , and , and use , , and for the three unit vectors. ANSWER: = -(mu_0/(4*pi))*(q*v /y_1^2)*x_unit Part D Find the magnetic field at the point . Part D.1 Evaluate the cross product To find the magnetic field for this part, it is convenient to use expression B from Part A: . Knowing and , find . Express your answer in terms of given quantities and , , and/or . ANSWER: = v*x1*y_unit
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Part D.2 Find the distance from the charge Part not displayed Express your answer in terms of , , , , , and , and use , , and for the three unit vectors. ANSWER: = (mu_0/(4*pi))*(q*v*x_1/(x_1^2 + z_1^2)^(3/2))*y_unit Part E The field found in this problem for a moving charge is the same as the field from a current element of length carrying current provided that the quantity is replaced by which quantity? Hint E.1 Hint not displayed ANSWER: i*dl [ Print ] [ Problem View ] Magnetic Field from Current Segments
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Description: Magnetic field calculations for z-axis as a function of currents in xy plane. Learning Goal: To apply the Biot-Savart law to find the magnetic field produced on the z axis from current elements in the xy plane. In this problem you are to find the magnetic field component along the z axis that results from various current elements in the xy plane (i.e., at ). The field at a point due to a current-carrying wire is given by the Biot-Savart law, , where and , and the integral is done over the current-carrying wire. Evaluating the vector integral will typically involve the following steps: Choose a convenient coordinate system--typically rectangular, say with coordinate axes , , and .
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