Problem 1
A +6.00-\(\mu\)C point charge is moving at a constant 8.00 \(\times\) 10\(^6\) m/s in the +\(y\)-direction, relative to a reference frame. At the instant when the point charge is at the origin of this reference frame, what is the magnetic- field vector \(\overrightarrow{B}\) it produces at the following points: (a) \(x =\) 0.500 m, \(y =\) 0, \(z =\) 0; (b) \(x =\) 0, \(y = -\)0.500 m, \(z =\) 0; (c) \(x =\) 0, \(y =\) 0, \(z = +\)0.500 m; (d) \(x =\) 0, \(y4 = -\)0.500 m, \(z = +\)0.500 m?
Problem 5
A -4.80-\(\mu\)C charge is moving at a constant speed of 6.80 \(\times\) 10\(^5\) m/s in the +\(x\) direction relative to a reference frame. At the instant when the point charge is at the origin, what is the magnetic-field vector it produces at the following points: (a) \(x =\) 0.500 m, \(y =\) 0, \(z =\) 0; (b) \(x =\) 0, \(y =\) 0.500 m, \(z =\) 0; (c) \(x =\) 0.500 m, \(y =\) 0.500 m, \(z =\) 0; (d) \(x =\) 0, \(y =\) 0, \(z =\) 0.500 m?
Problem 10
A short current element \(\overrightarrow{dl}\) S = (0.500 mm)\(\hat{\imath}\) carries a current of 5.40 A in the same direction as \(\overrightarrow{dl}\). Point P is located at \(\overrightarrow{r} =\) (-0.730 m)\(\hat{\imath}\) + (0.390 m)\(\hat{k}\) . Use unit vectors to express the magnetic field at \(P\) produced by this current element.
Problem 11
A long, straight wire lies along the \(z\)-axis and carries a 4.00-A current in the \(+z\)-direction. Find the magnetic field (magnitude and direction) produced at the following points by a 0.500-mm segment of the wire centered at the origin: (a) \(x =\) 2.00 m, \(y = 0\), \(z =\) 0; (b) x = 0, \(y =\) 2.00 m, \(z =\) 0; (c) \(x =\) 2.00 m, \(y =\) 2.00 m, \(z =\) 0; (d) \(x\) = 0, \(y\) = 0, \(z\) = 2.00 m,
Problem 14
A square wire loop 10.0 cm on each side carries a clockwise current of 8.00 A. Find the magnitude and direction of the magnetic field at its center due to the four 1.20-mm wire segments at the midpoint of each side.
Problem 15
Lightning bolts can carry currents up to approximately 20 kA. We can model such a current as the equivalent of a very long, straight wire. (a) If you were unfortunate enough to be 5.0 m away from such a lightning bolt, how large a magnetic field would you experience? (b) How does this field compare to one you would experience by being 5.0 cm from a long, straight household current of 10 A?
Problem 16
A very long, straight horizontal wire carries a current such that 8.20 \(\times\) 10\(^{18}\) electrons per second pass any given point going from west to east. What are the magnitude and direction of the magnetic field this wire produces at a point 4.00 cm directly above it?
Problem 17
The body contains many small currents caused by the motion of ions in the organs and cells. Measurements of the magnetic field around the chest due to currents in the heart give values of about 10 \(\mu\)G. Although the actual currents are rather complicated, we can gain a rough understanding of their magnitude if we model them as a long, straight wire. If the surface of the chest is 5.0 cm from this current, how large is the current in the heart?
Problem 18
Certain bacteria (such as \(Aquaspirillum\) \(magnetotacticum\)) tend to swim toward the earth's geographic north pole because they contain tiny particles, called magnetosomes, that are sensitive to a magnetic field. If a transmission line carrying 100 A is laid underwater, at what range of distances would the magnetic field from this line be great enough to interfere with the migration of these bacteria? (Assume that a field less than 5\(\%\) of the earth's field would have little effect on the bacteria. Take the earth's field to be 5.0 \(\times\) 10\(^{-5}\) T, and ignore the effects of the seawater.)
Problem 19
(a) How large a current would a very long, straight wire have to carry so that the magnetic field 2.00 cm from the wire is equal to 1.00 G (comparable to the earth's northward-pointing magnetic field)? (b) If the wire is horizontal with the current running from east to west, at what locations would the magnetic field of the wire point in the same direction as the horizontal component of the earth's magnetic field? (c) Repeat part (b) except the wire is vertical with the current going upward.
