Explanation 1) Concept: We know from the Faraday’s law that the changing magnetic field can induce an emf. Therefore, the rate of change of magnetic field is equal to the induced emf. By using the data from the given plot, we can find the rate of change of magnetic field in both the regions. We can find if the magnitude of B 2 → is increasing or decreasing by considering the Lenz’s law. 2) Formula: i) ε i n d = - d ϕ B d t ii) ϕ B = ∮ B → · d A → 3) Given: i) Radius of region 1 , r 1 = 1.0 c m = 1 × 10 - 2 m ii) Radius of region 2 , r 2 = 2.0 c m = 2 × 10 - 2 m iii) Rate of change of magnetic field in region 1 , i.e. d B 1 d t , is increasing in magnitude iv) Vertical scale, ε s = 20 n V 4) Calculations: a) Let’s find the slope m 1 from the graph, showing variation of ε verses R 2 in the region 1 m 1 = ε R 2 = 8.0 - 0.0 1.0 - 0.0 · n V c m 2 = 8.0 n V c m 2 Similarly, for the region 2, we get m 2 = ε R 2 = 20.0 - 8.0 4.0 - 1.0 · n V c m 2 = 12 3 n V c m 2 = 4.0 n V c m 2 Now from Faraday’s law, induced emf is given as ε i n d = - d ϕ B d t = - A · d B d t Taking the magnitude we have | ε i n d | = d ϕ B d t = A · d B d t Where A is the area attached to the loop along which we intend to find the emf

10th Edition

ISBN: 9781118230725

Author: David Halliday, Robert Resnick, Jearl Walker

Publisher: Wiley, John & Sons, Incorporated

See similar textbooks

Concept explainers

Magnetic Force

A magnetic force arises when a charged particle or a current-carrying conductor is placed in a magnetic field. It is created because of the movement of the charged particles.

Question

Chapter 30, Problem 84P

To determine

To find:

a) Rate of change of magnetic field in region 1,dB1dt

b) Rate of change of magnetic field in region 2,dB2dt

c) If the magnitude of B2→ is increasing or decreasing.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 30, Problem 83P

Chapter 30, Problem 85P

Students have asked these similar questions

A long thin solenoid has 779 turns per meter and radius 2.00cm. The current in the solenoid is increasing at a rate 23 A/s. What is the magnitude of the induced Electric field (in V/m) at a point near the center of the solenoid and 1.3 cm from its axis?

A circular coil that has N = 280 turns and a radius of r = 11.0 cm lies in a magnetic field that has a magnitude of Bo = 0.0625 T directed perpendicular to the plane of the coil. What is the magnitude of the magnetic flux B through the coil? OB = T-m2 The magnetic field through the coil is increased steadily to 0.175 T over a time interval of 0.360 s. What is the magnitude |E| of the emf induced in the coil during the time interval? |E| = V Question Sou

A circular wire loop of radius 5 cm resides in a constant magnetic field of 500 Tesla. The direction of the magnetic field is perpendicular to the plane containing the wire loop. What is the magnitude of the electric field induced by this magnetic field? O O N/C O 2500 N/C O 0.01 V/m O 100 V/m

Chapter 30 Solutions

Fundamentals of Physics Extended

Ch. 30 - If the circular conductor in Fig. 30-21 undergoes...Ch. 30 - Prob. 2Q Ch. 30 - Prob. 3Q Ch. 30 - Prob. 4Q Ch. 30 - Prob. 5Q Ch. 30 - Prob. 6Q Ch. 30 - Prob. 7Q Ch. 30 - Prob. 8Q Ch. 30 - Prob. 9Q Ch. 30 - Prob. 10Q

Ch. 30 - Figure 30-31 shows three situations in which a...Ch. 30 - Figure 30-32 gives four situations in which we...Ch. 30 - Prob. 1P Ch. 30 - A certain elastic conducting material is stretched...Ch. 30 - Prob. 3P Ch. 30 - A wire loop of radius 12 cm and resistance 8.5 is...Ch. 30 - Prob. 5P Ch. 30 - Figure 30-37a shows a circuit consisting of an...Ch. 30 - In Fig. 30-38, the magnetic flux through the loop...Ch. 30 - Prob. 8P Ch. 30 - Prob. 9P Ch. 30 - Prob. 10P Ch. 30 - A rectangular coil of N turns and of length a and...Ch. 30 - Prob. 12P Ch. 30 - Prob. 13P Ch. 30 - GO In Fig. 30-42a, a uniform magnetic field B...Ch. 30 - GO A square wire loop with 2.00 m sides is...Ch. 30 - GO Figure 30-44a shows a wire that forms a...Ch. 30 - A small circular loop of area 2.00 cm2 is placed...Ch. 30 - Prob. 18P Ch. 30 - ILW An electric generator contains a coil of 100...Ch. 30 - At a certain place, Earths magnetic field has...Ch. 30 - Prob. 21P Ch. 30 - A rectangular loop area = 0.15 m2 turns in a...Ch. 30 - SSM Figure 30-47 shows two parallel loops of wire...Ch. 30 - Prob. 24P Ch. 30 - GO Two long, parallel copper wires of diameter 2.5...Ch. 30 - GO For the wire arrangement in Fig. 30-49, a =...Ch. 30 - ILW As seen in Fig. 30-50, a square loop of wire...Ch. 30 - Prob. 28P Ch. 30 - Prob. 29P Ch. 30 - Prob. 30P Ch. 30 - Prob. 31P Ch. 30 - A loop antenna of area 2.00 cm2 and resistance...Ch. 30 - GO Figure 30-54 shows a rod of length L = 10.0 cm...Ch. 30 - Prob. 34P Ch. 30 - Prob. 35P Ch. 30 - Prob. 36P Ch. 30 - Prob. 37P Ch. 30 - Prob. 38P Ch. 30 - Prob. 39P Ch. 30 - Prob. 40P Ch. 30 - A circular coil has a 10.0 cm radius and consists...Ch. 30 - Prob. 42P Ch. 30 - Prob. 43P Ch. 30 - Prob. 44P Ch. 30 - Prob. 45P Ch. 30 - Prob. 46P Ch. 30 - Inductors in series. Two inductors L1 and L2 are...Ch. 30 - Prob. 48P Ch. 30 - Prob. 49P Ch. 30 - Prob. 50P Ch. 30 - ILW The current in an RL circuit drops from 1.0 A...Ch. 30 - Prob. 52P Ch. 30 - Prob. 53P Ch. 30 - Prob. 54P Ch. 30 - Prob. 55P Ch. 30 - Prob. 56P Ch. 30 - In Fig. 30-65, R = 15 , L = 5.0 H, the ideal...Ch. 30 - Prob. 58P Ch. 30 - Prob. 59P Ch. 30 - Prob. 60P Ch. 30 - Prob. 61P Ch. 30 - A coil with an inductance of 2.0 H and a...Ch. 30 - Prob. 63P Ch. 30 - Prob. 64P Ch. 30 - Prob. 65P Ch. 30 - A circular loop of wire 50 mm in radius carries a...Ch. 30 - Prob. 67P Ch. 30 - Prob. 68P Ch. 30 - ILW What must be the magnitude of a uniform...Ch. 30 - Prob. 70P Ch. 30 - Prob. 71P Ch. 30 - Prob. 72P Ch. 30 - Prob. 73P Ch. 30 - Prob. 74P Ch. 30 - Prob. 75P Ch. 30 - Prob. 76P Ch. 30 - Prob. 77P Ch. 30 - Prob. 78P Ch. 30 - SSM In Fig. 30-71, the battery is ideal and = 10...Ch. 30 - Prob. 80P Ch. 30 - Prob. 81P Ch. 30 - A uniform magnetic field B is perpendicular to the...Ch. 30 - Prob. 83P Ch. 30 - Prob. 84P Ch. 30 - Prob. 85P Ch. 30 - Prob. 86P Ch. 30 - Prob. 87P Ch. 30 - Prob. 88P Ch. 30 - A coil with an inductance of 2.0 H and a...Ch. 30 - Prob. 90P Ch. 30 - Prob. 91P Ch. 30 - Prob. 92P Ch. 30 - Prob. 93P Ch. 30 - A long cylindrical solenoid with 100 turns/cm has...Ch. 30 - Prob. 95P Ch. 30 - A square loop of wire is held in a uniform 0.24 T...Ch. 30 - Prob. 97P Ch. 30 - The inductance of a closely wound coil is such...Ch. 30 - The magnetic field in the interstellar space of...Ch. 30 - Prob. 100P Ch. 30 - A toroid has a 5.00 cm square cross section, an...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

a) Rate of change of magnetic field in region 1 , d B 1 d t b) Rate of change of magnetic field in region 2 , d B 2 d t c) If the magnitude of B 2 → is increasing or decreasing.

Solution Summary: The author explains that changing magnetic field can induce an emf, so the rate of change is equal to it.

Concept explainers

To find:

a) Rate of change of magnetic field in region 1,dB1dt

b) Rate of change of magnetic field in region 2,dB2dt

c) If the magnitude of B2→ is increasing or decreasing.

Want to see the full answer?

Chapter 30 Solutions

a) Rate of change of magnetic field in region 1 , d B 1 d t b) Rate of change of magnetic field in region 2 , d B 2 d t c) If the magnitude of B 2 → is increasing or decreasing.

Solution Summary: The author explains that changing magnetic field can induce an emf, so the rate of change is equal to it.

Concept explainers

To find: a) Rate of change of magnetic field in region 1,dB1dt b) Rate of change of magnetic field in region 2,dB2dt c) If the magnitude of B2→ is increasing or decreasing.

Want to see the full answer?

Chapter 30 Solutions

To find:

a) Rate of change of magnetic field in region 1,dB1dt

b) Rate of change of magnetic field in region 2,dB2dt

c) If the magnitude of B2→ is increasing or decreasing.