33 1 Model A magnetic field is caused by an electric current Visualize Please refer to Figure EX33 1 Solve The magnitude of the magnetic field at point 1 is 2 0 mT and its direction can be determined by using the right hand rule Grab the current carrying wire so that your thumb points in the direction of the current 2 0 mT into the page At point 2 the magnetic field Because your fingers at point 1 point into the page due to the bottom wire is into the page The right hand rule tells us that the magnetic field from the top wire is also into the page At point 2 4 0 mT into the page cid 71 2B cid 71 1B 33 2 Model A magnetic field is caused by an electric current Visualize Please refer to Figure EX33 2 Solve The current in the wire is directed to the right B2 20 mT 20 mT 40 mT because the two overlapping wires are carrying current in the same direction and each wire produces a magnetic field having the same direction at point 2 B3 20 mT 20 mT 0 mT because the two overlapping wires carry currents in opposite directions and each wire produces a field having opposite directions at point 3 The currents at 4 are also in opposite directions but the point is to the right of one wire and to the left of the other From the right hand rule the field of both currents is out of the page Thus B4 20 mT 20 mT 40 mT 33 3 Model The magnetic field is that of a moving charged particle Visualize The first point is on the x axis with a 90 The second point is on the y axis with b 180 and the third point is on the y axis with c 0 Solve a Using Equation 33 1 the Biot Savart law the magnetic field strength is 10 T m A 1 60 10 7 C 1 0 10 m s sin 90 qv 7 19 1 60 10 15 T B a 0 4 sin 2 r 1 0 10 m 2 2 cid 71 To use the right hand rule for finding the direction of B cid 71 and v cid 71 cid 71 is perpendicular to the plane of r field vector B In the present case the fingers point along the k direction Thus b Bb 0 T because sin b sin 180 0 c Bc 0 T because sin c sin 0 0 point your thumb in the direction of The magnetic cid 71 v and points in the same direction that your fingers point cid 71 B a 1 60 10 15 k T 33 4 Model The magnetic field is that of a moving charged particle Visualize 19 1 0 10 m 2 2 cid 71 a B cid 71 aB The first point is on the x axis with a 90 The second point is on the z axis with b 0 and the third point is in the yz plane with c 45 Solve a Using Equation 33 1 the Biot Savart law the magnetic field strength is 10 T m A 1 60 10 7 C 2 0 10 m s sin 90 qv 7 3 2 10 15 T B a 0 4 sin 2 r To use the right hand rule for finding the direction of point your thumb in the direction of Your fingers points along the y axis Thus 3 2 10 15 j T cid 71 v cid 71 B a point along the y axis but since the charge is negative b Bb 0 T because sin b sin 0 0 c For the third point B c 7 10 T m A 1 60 10 1 0 10 m 2 2 7 C 2 0 10 m s sin 45 1 0 10 m 2 2 19 cid 71 cB cid 71 is perpendicular to the plane formed by r and cid 71 B c cid 71 v along the x axis but because the charge is negative 1 13 10 15 i T 1 13 10 15 T The right hand rule gives the direction of cid 71 r The direction of cid 71 v 33 5 Model The magnetic field is that of a moving charged particle Visualize Please refer to Figure EX33 5 Solve Using the Biot Savart law B 0 4 qv sin 2 r 7 10 T m A 1 60 10 1 0 10 m 2 2 7 C 2 0 10 m s sin 45 1 0 10 m 2 2 19 1 13 10 15 T cid 71 The right hand rule applied to the proton points B into the page Thus 1 13 10 15 k T cid 71 B 33 6 Model The magnetic field is that of a moving charged particle Visualize Please refer to Figure EX33 6 Solve The Biot Savart law is 10 T m A 1 60 10 2 0 10 m 2 0 10 m 7 C 2 0 10 m s sin135 0 4 sin 2 r qv B 2 7 2 19 2 2 The right hand rule for the positive charge indicates the field points out of the page Thus 2 83 10 16 T cid 71 B 2 83 10 16 k T 33 7 Model The magnetic field is that of a moving proton Visualize The magnetic field lies in the xy plane Solve Using the right hand rule the charge is moving along the z direction That is Savart law cid 71 v vk Using the Biot B 0 4 qv sin 2 r 1 0 10 13 T 7 10 T m A 1 60 10 1 0 10 m 3 19 2 C sin 90 v v 6 3 10 m s in the z direction 6 33 8 Model The magnetic field is that of an electric current in a long straight wire Solve From Example 33 3 the magnetic field strength of a long straight wire carrying current I at a distance d from the wire is B wire 0 2 I d The current needed to produce the earth s magnetic field is calculated as follows B earth surface 5 5 10 T I 2 5 A 7 2 10 T m A I 0 010 m Likewise the currents needed for a refrigerator magnet a laboratory magnet and a superconducting magnet are 250 A 5000 50 000 A and 500 000 A 33 9 Model The magnetic field is that of an electric current in a long straight wire Solve From Example 33 3 the magnetic field strength of a long straight wire carrying current I at a distance d from the wire is B 0 2 I d The distance d at which the magnetic field is equivalent to Earth s magnetic field is calculated as follows B earth surface 5 5 10 T 7 2 10 T m A d 4 0 cm 10 A d Likewise the corresponding distances for …
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