An increasing number of products, such as passports and credit cards, contain an

Question

An increasing number of products, such as passports and credit cards, contain an embedded radio-frequency identification chip that both stores and transmits information. The chips do not have their own power sources. Instead, they receive their power through induction from the device used to read the stored information. The reading device generates a magnetic field, and the passport or credit card containing a coil is passed through this field.

If a certain chip needs a peak induced emf of 3.0 V to operate and the magnetic field varies with time as B(t)=Bpeaksin(t), where Bpeak = 6.0 mT is the maximum magnetic field and = 8.52 × 107 s1,what value must the product AN have in order for the chip to operate, where A is the coil's surface area and N is number of turns in the coil?

Explanation / Answer

B(t)=Bpeak sin(t)

B(t)=(0.006) sin(8.52 x 107t)

taking derivative relative to "t" both side

dB(t) / dt = (51.12 x 104) Cos(8.52 x 107t)

Induced EMf is given as

E = NBA w

3 = (NA) (0.006) (8.52 x 107)

NA = 5.87 x 10-6

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