Magnetic Field Practice Problems
1. Consider the current carrying wires which lie in the plane of the paper as shown below. The semicircular loop at the top consists of a circular arc which extends over an angle of 90o and carries a current I. The inner arc has a radius 3L and the outer arc has a radius 6L and each is placed so that their centers are at point P. An infinite line of current is placed a perpendicular distance of 2L from point P. The directions of the currents are shown in the figure.
a)Find the magnitude and direction of the magnetic field at point P.
b) A charge of 4.5x10-7 C arrives at point P with a velocity of v=500m/si+800m/sj. Find the force on the charge.
2. Consider the straight current segments which lie in a constant magnetic field as shown below. The magnetic field has a magnitude of 4.5 T which points out of the paper. The lengths of the segments are shown.
Find the net vector force acting on the current segments.
3. Consider a 1000 kg vehicle which levitates using magnetic forces. The vehicle is in a uniform field of 7 x 10-5 T pointing north ( B = -Bo k) due to the earth’s field. The ship can generate a current running along a 5 m wire from the back of the ship to the front of the ship You must draw the directions of all quantities or use proper unit vectors to clarify your solutions. Assume the vehicle is oriented for maximum force.
a) In what direction must the ship be pointing in order to achieve the maximum force?
b) How much current must be provided in order to levitate (or float) the vehicle?
c) How much current must flow to produce a downward acceleration of a=-15 m/s2 j?
d) Find the net force on a charge of 1 Coulomb if it thrown out of the window with a velocity of v = (200i + 200j) m/s.
4. Two long straight wires are spaced a distance of 0.8 m apart, as shown below. The wires carry different currents in opposite directions as indicated in the diagram.
Q
a) Find the direction and magnitude of the magnetic field at point P, which is located 0.5 m below I1. Briefly explain how you determined the direction of the field.
b) Find the direction and magnitude of the magnetic field at point Q, which is located a distance of 0.4 m below the lower wire.
c) Calculate the force on a charge of 200 C which is moving at 100 m/s into the paper at point P. Be sure to show your work or justify your answer clearly.
5. A current carrying wire is bent into two segments of length 0.5 m and height 0.2 m, which lie in the xy plane as shown below. There is a uniform magnetic field Bo=3 T k perpendicular to the plane of the loop.
y
Find the net force( magnitude and direction) acting on the wire.
6. Consider the current carrying wires shown below. The loop at the bottom consists of arc segments which extend over an angle of 120o and carry a current I. The inner arc has a radius R and the outer arc has a radius 2R and each is placed so that their centers are at point P. An infinite line of current 2I is placed horizontally a distance 2.5R above point P as shown. The directions of the currents are shown in the figure. Find the magnitude and direction of the magnetic field at point P.
7. Consider the two infinite current carrying wires which are placed a distance D=0.2 m and lie along the x-axis. The top wire carries a current of 3 A, and the bottom has a current of 5A. Both currents flow to the right.
D=0.2 m
a) Calculate the magnetic field (magnitude and direction) at point P, which is located directly in between the two wires.
b) Calculate the magnetic field at point Q, which is located 0.2 m above the upper wire.
c) A charge of 2x10-9 C is introduced in between the wires. If it has a velocity v=2i +3j when it reaches the point directly in-between the wires, calculate the resulting vector force on the charge.
8. Consider the coaxial arrangement of conductors shown below. The inner conductor is a wire of radius a and the outer cylindrical shell has an inner radius b and outer radius c. On one end, the cylinder and wire are connected to a source of potential difference. At the other end, the wire is connected to the positive terminal of a battery and the cylinder is connected to the negative end so that there is a current I traveling down the wire and back up the shell.
Find the magnetic field (magnitude and direction) at all points in space a) r < a, b) b > r > a, c) c > r > b, d) r > c .