Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
17.4k views
in Physics by (80.8k points)

A circular loop of wire of resistance 0.2 ohm encloses an area 0.3 square meter and lies flat on a wooden table as shown above. A magnetic field that varies with time t as shown below is perpendicular to the table. A positive value of B represents a field directed up from the surface of the table; a negative value represents a field directed into the tabletop.

a. Calculate the value of the magnetic flux through the loop at time t = 3 seconds.

b. Calculate the magnitude of the emf induced in the loop during the time interval t = 0 to 2 seconds.

c. On the axes below, graph the current I through the coil as a function of time t, and put appropriate numbers on the vertical scale. Use the convention that positive values of I represent counterclockwise current as viewed from above.

1 Answer

+1 vote
by (52.5k points)
selected by
 
Best answer

(a) Ф = BA, read B from the graph at 3 seconds and use the given area (0.2)(0.3) = 0.06 Wb

(b) Induced emf = ε = NΔФ/t … = 1*(BAf – BAi) / t = A(Bf – Bi) / t = (0.3)(0.2 – (–0.2)) / 2 = 0.06 V

(c) First, the directions are found based on Lenz Law. From 0–1 the downward flux is decreasing so current flows CW to add back the downward field. Then we hit zero flux at 1 second. Moving 1–2 seconds we want to maintain the zero flux and we have an increasing upwards flux so the current still flows CW to add downward field to cancel the gaining flux. At 2 seconds the flux becomes constant so current does not flow up until 4 seconds. From 4–6 seconds we are loosing upwards flux so current flows CCW to add back that upwards field.

To determine the current magnitudes. Use V=IR.

From 0–2 sec. 0.06 = I (0.2) I = 0.3 A

From 2–4, I=0.

From 4–6, first determine new emf. Since the slope is half as much as 0–2 sec, the emf should be half as much as well. Then V=IR … 0.03 = I (0.2) I = 0.15 A

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...