Faraday's law worksheet with answers

Can you help me understand this Physics question?

This HW is about Faraday's Law, and you can just follow instructions in the word file and type answers in the file or write them in a paper.1 FARADAY’S LAW PHYSICS OBJECTIVES AND READINGS Physics objectives: The complete list of PHYS 251 course objectives is on Angel. This assignment focus on 5. Electromagnetism and Electromagnetic Waves, including a. determining the induced electric field, EMF, and/or current due to a changing magnetic flux (Faraday’s Law and Lenz’s law) Names: ____________________________ ____________________________ ____________________________ Readings: Knight Chap 32.1- 32.6 Section #______________ Date: _____________ Useful Equations & Concepts ⃗ is defined as: 𝛷𝐵 = ∫ 𝐵 ⃗ ⋅ 𝑑𝐴 The magnetic flux 𝛷𝐵 through an area in a magnetic field 𝐵 Faraday's Law of Induction: If the magnetic flux through a closed conducting loop changes with time, a current and an emf are produced in the loop: ℇ= − 𝑑𝛷𝐵 𝑑𝑡 Lenz's Law: The current induced by a changing magnetic flux has a direction such that the magnetic field created by the induced current opposes the change in the original magnetic field. 2 EXERCISE 1: FARADAY’S LAW WARM -UP Five loops are formed of copper wire of the same gauge (same cross-sectional area). Loops 1–4 are identical; loop 5 has the same height as the others but is longer. At the instant shown, all the loops are moving at the same speed in the directions indicated. 1 2 There is a uniform magnetic field pointing out of the page in Region I; in Region II there is no magnetic field. Ignore any interactions between the loops. 1. 3 For each loop that has an induced current, determine the direction (e.g. clockwise vs. counter-clockwise) of that current using Lenz’ Law. 4 5 Region I 2. Region II Rank the magnitudes of the induced emfs around the loops. Explain your reasoning analytically. Hint: Consider each rectangle as having an area in Region 1 equal to 𝐴 = 𝑥 ℎ where ℎ is the height and 𝑥 is the portion of the length that is inside Region 1. 3. Rank the magnitudes of the currents in the loops. Explain your reasoning analytically 3 EXERCISE 2: LOOP IN NON-UNIFORM B FIELD In each of the cases considered below, the position of a conducting loop is shown at two times, t0 and t0 + Δt. The loop starts from rest in each case at t = t0 and is displaced to the right in Case A and to the left in Case B. Make sure you understand the meaning of the magnetic field lines before starting to think about the questions below 4. Assuming that the loop moves at constant speed and using the magnetic field lines as a guide, determine the following in each case: a. What is the current in the loop before it starts moving? Explain your answer. 5. As the loop is moving, what is the direction of the induced magnetic field of the loop? Explain your answer. 4 6. As the loop is moving, what is the direction of the induced current in the loop at the top of the loop (into the page or out of the page)? Explain your answer EXERCISE 3: THE ELECTRIC GENERATOR w A circular loop of area A is made to spin with angular velocity  in a region of uniform B field that is out of the page and has magnitude B. We will start our clock (t = 0) when the loop is laying flat in the plane of the page, as shown below B 7. What is the magnetic flux through the loop as a function of ⃗ ⋅ 𝑑𝐴 = ∫ 𝐵 𝑑𝐴 cos () , where A is the time? Recall 𝛷𝐵 = ∫ 𝐵 area of the circular loop. (Hint: what is  in this case? ) wt = 0 8.