Suppose the magnetic flux density linking the loop of Fig (Example) is given by B = –zˆ0.3...

Suppose the magnetic flux density linking the loop of Fig (Example) is given by B = –zˆ0.3e-1 (T). What would the direction of the current be, relative to that shown in Fig. for t ≥ 0?

Example: Lenz’s Law

Determine voltages V1 and V2 acros; the 2-Ω and 4-Ω resistors shown,in Fig. The loop is located in the x-y plane, its area is 4 m2. the magnetic flux density is B= –zˆ0.3t (T). and the internal resistance of the wire may be ignored.

Solution:

The flux flowing through the loop is

= –0.3t × 4 = –1.2t (Wb),

and the corresponding transformer emf is

Since the magnetic flux through the loop is along the –z-direction (into the page) and increases in magnitude with time t. Lenz’s law states that the induced current I should he in a direction such that the magnetic flux density Bind it induces counteracts the direction of change Φ Hence. I has to be in the direction shown in the circuit because the corresponding Bind is along the + z-direction in the region inside the loop area. This, in turn, means that V1 and V2 are positive voltages. Thc total voltage ot 1.2 V is distributed across two resistors in series. Consequently.

W, – I R1 = 0.2 × 2 = 0.4 V.V2 = I R2 = 0.2 × 4 = 0.8 V.

Figure