30.4.1 Using Lenz’s Law
FIGURE 30.21 shows six basic situations. The magnetic field can point either up or down through the loop. For each, the flux can either increase, hold steady, or decrease in strength. These observations form the basis for a set of rules about using Lenz’s law.
FIGURE 30.21 The induced current for six different situations.
TACTICS BOX 30.1 Using Lenz’s law
1 Determine the direction of the applied magnetic field. The field must pass through the loop.
2 Determine how the flux is changing. Is it increasing, decreasing, or staying the same?
3 Determine the direction of an induced magnetic field that will oppose the change in the flux.
Increasing flux: the induced magnetic field points opposite the applied magnetic field.
Decreasing flux: the induced magnetic field points in the same direction as the applied magnetic field.
Steady flux: there is no induced magnetic field.
4 Determine the direction of the induced current. Use the right-hand rule to determine the current direction in the loop that generates the induced magnetic field you found in step 3.
Workbook Exercises 10–14
Let’s look at two examples.
EXAMPLE 30.6 Lenz’s law 1
FIGURE 30.22 shows two loops, one above the other. The upper loop has a battery and a switch that has been closed for a long time. How does the lower loop respond when the switch is opened in the upper loop?
FIGURE 30.22 The two loops of Example 30.6.
MODEL We’ll use the right-hand rule to find the magnetic fields of current loops.
SOLVE FIGURE 30.23 shows the four steps of using Lenz’s law. Opening the switch induces a ccw current in the lower loop. This is a momentary current, lasting only until the magnetic field of the upper loop drops to zero.
FIGURE 30.23 Applying Lenz’s law.
REVIEW The conclusion is consistent with Figure 30.21.
EXAMPLE 30.7 Lenz’s law 2
FIGURE 30.24 shows two coils wrapped side by side on a cylinder. When the switch for coil A is closed, does the induced current in coil B pass from right to left or from left to right through the current meter?
FIGURE 30.24 The two coils of Example 30.7.
MODEL We’ll use the right-hand rule to find the magnetic field of a coil.
VISUALIZE It is very important to look at the direction in which a coil is wound around the cylinder. Notice that the two coils in Figure 30.24 are wound in opposite directions.
SOLVE FIGURE 30.25 shows the four steps of using Lenz’s law. Closing the switch induces a current that passes from right to left through the current meter. The induced current is only momentary. It lasts only until the field from coil A reaches full strength and is no longer changing.
FIGURE 30.25 Applying Lenz’s law.
REVIEW The conclusion is consistent with Figure 30.21.