Problems in Magnetism 07/20/2005

1Magnetism1.) Two 853.9 m long wires run parallel to each other separated by 30.45 mm and with a force between them of0.0286 N. If one of them carries a currents of 1.978 A, what is the current in the other?2.)A wire having a mass per unit length of 0.500 g/cm carries a 2.00 A current horizontally to the south.What are the direction and magnitude of the minimum magnetic field needed to lift this wire vertically upward?3.)A rectangular coil (0.2m x 0.8 m) has 200 turns of wire and is in a uniform magnetic field of 0.3 T. If theorientation of the coil is varied through all possible positions, the maximum torque on the coil by magnetic forces is0.08 Nm. What is the current in the coil?4.)A cosmic-ray proton in interstellar space has kinetic energy of 1.6x10 −12 J and executes a circular orbithaving a radius equal to that of Mercury’s orbit around the sun (5.8x10 10 m). What is the magnetic field in thatregion?5.)Two long, parallel conductors carry currents I1 = 3.00 A and I2 = 3.00 A, both directed into the page inthe figure below. Determine the magnitude and direction of the resultant magnetic field at P.6.)A solenoid 2.50 cm in diameter and 30.0 cm long has 300 turns and carries 12.0 A. Determine the magneticfield inside the solenoid.7.) A long, tightly wound solenoidal coil of radius R = 0.30 m has its axis along the z direction and currentwhich flows counter-clockwise in the drawing below, resulting in a magnetic field of magnitude B = 0.55 T. a)Whatis the direction of the field B ? b.) An electron moves with velocity v = 5.010 6 m/s in the y direction in side thesolenoid. Determine the force (magnitude and direction) on the electron at this point.8.)A very long, straight wire carries a current I=7.5 A directed upward . a)Use Amperes Law to find the directionand magnitude of the magnetic field at a perpendicular distance 25 am from the wire. b)A second wire isplaced parallel to the first wire at P which carries a current I=3 A directed downward. Determine the direction ofthe force on the second wire and calculate the force per unit length.9.) A circular wire loop of diameter d = 10.0 cm and resistance 2.0 ohm is placed in a region with a uniformmagnetic field pointing inside the plane of the paper. Find the direction and magnitude of any current in theloop if B = 0.32 T and is constant.10.)An electron has a velocity of 6.0x10 6 m/s in the positive x direction. The magnetic field at the point ofinterest has components, Bx= 3.0 T, By = 1.5 T. What is the magnitude of the acceleration of the electron at thispoint ? (mass of electron = 9.1x10 −31 kg)11.)Two long straight parallel wires separated by a distance of 20 cm carry currents of 30 A and 40 A in oppositedirections. What is the magnitude of the resulting magnetic field at a point that is 15 cm from the wire carrying the30 A current and 25 cm from the other wire? (no typos here - the point of interest is NOT in the plane of the two wires)

212.)What is the magnitude of the magnetic force on a charged particle (Q = 5.0 microC) moving with aspeed of 80 km/s in the positive x direction at a point where Bx = 5.0 T, By = -4.0 T, and Bz = 3.0 T ?13.)A uniform magnetic field B, with magnitude B = 1.2x10 −3 T, points vertically upward throughout thevolume of a laboratory chamber. A proton with a velocity v = 3.2x10 7 m/s enters the laboratory moving horizontallyfrom south to north. Find (a) the magnitude and (b) the direction of magnetic force on the proton.14.)A proton moves in a uniform magnetic field B with a speed of 10 7 m/s and experiences an accelerationof 2x10 13 m/s2 in the +X-direction when its velocity is in the +Z-direction. Determine the magnitude and directionof the magnetic field for which the magnitude of the field is a minimum.15.)An electron moves with a speed v = 2x10 7 m/s through a magnetic field of B = 0.080 N-s/C-m. (a)What are the greatest and smallest forces the magnetic field may exert on the electron? (b) If the acceleration ofthe electron is 1.41x10 1 7 m/s2, what angle does the velocity make with the magnetic field? The electron has a massm = 9.1x10 −31 kg and its charge e = 1.6x10 −19 .16.)A particle of charge q = 10 −6 C moves to the right with velocity v = 10 3 m/s in a magnetic field B = 2N-s/C-m which makes an angle of 30 with v. Find the magnitude of the force on the charged particle.