The figure illustrates the lengthwise cross-section of a current-carrying coil. This coil carries a current \( I \) and contains \( N \) evenly spaced turns along its length \( l \). The illustration presents a portion of this coil with different paths marked as A, B, C, and D.**Paths and Directions:**- **Path A:** A rectangular path surrounding a single turn of the coil.- **Path B:** A rectangular path at the end of the coil, enclosing no current.- **Path C:** A rectangular path that encircles multiple turns of the coil.- **Path D:** Another complex path around multiple turns.**Tasks:**a. **Evaluate \(\oint \mathbf{B} \cdot d\mathbf{l}\) along path A.** Give your answer in terms of current \( I \), constant \(\mu_0\), and any numerical constants. **Additional hint:** \[ \oint_A \mathbf{B} \cdot d\mathbf{l} = \underline{\hspace{3cm}} \] *(Format hint: Spell out Greek letters and use an underscore ("_") for subscripts. For example, to type in \(\mu_0\), type in "mu_0".)*b. **Evaluate \(\oint \mathbf{B} \cdot d\mathbf{l}\) along path B.** **Hint for (b):** \[ \oint_B \mathbf{B} \cdot d\mathbf{l} = \underline{\hspace{3cm}} \]c. **Evaluate \(\oint \mathbf{B} \cdot d\mathbf{l}\) along path C.** **Additional hints for (c) and (d):** \[ \oint_C \mathbf{B} \cdot d\mathbf{l} = \underline{\hspace{3cm}} \]d. **Evaluate \(\oint \mathbf{B} \cdot d\mathbf{l}\) along path D.** \[ \oint_D \mathbf{B} \cdot d\mathbf{l} = \underline{\hspace{3cm}} \]**Explanations:**- The task involves calculating the line integral of the

By ampere's law Integral of B.dl = u0Iin

The figure below shows the lengthwise cross-section of a current-carrying coil. The coil carries a current of I, and there are N evenly space turns along the length I of the coil. The figure shows a portion of this coil. A В Hints a. Evaluate · dl along path A. Give your answer in terms of current I, constant uo, and any numerical constants. Additional hint for (a) f B . dī - (Format hint: Spell out Greek letters and use underscore ("_") for subscripts. For example, to type in Ho, type in "mu_0".) b. Evaluate B · di along path B. Hint for (b) f B. di- B c. Evaluate PB · dl along path C. Additional hints for (c) and (d) B. dī f - d. Evaluate • dl along path D. f B - di-

The figure below shows the lengthwise cross-section of a current-carrying coil. The coil carries a current of I, and there are N evenly space turns along the length I of the coil. The figure shows a portion of this coil. A В Hints a. Evaluate · dl along path A. Give your answer in terms of current I, constant uo, and any numerical constants. Additional hint for (a) f B . dī - (Format hint: Spell out Greek letters and use underscore ("_") for subscripts. For example, to type in Ho, type in "mu_0".) b. Evaluate B · di along path B. Hint for (b) f B. di- B c. Evaluate PB · dl along path C. Additional hints for (c) and (d) B. dī f - d. Evaluate • dl along path D. f B - di-

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Related questions

Q: I could really use some help on some questions! The problem is as follows: A thine wire of length…

Q: In the following figures, each conductor carries 2.0 A of current into or out of the page. Draw a…

A: The above problem can be solved by using Ampere's Circuital Law. According to this law

Q: Here, an infinite constant current travels to the right. There are 3 independent single loops of…

A: Given, Here, an infinite constant current travels to the right. There are 3 independent single loops…

Q: 4. In the rectangular wire of length I and width w, there is a uniform magnetic field B = Bosin?wt…

Q: A coaxial cable consists of a long hollow cylindrical wire (inner radius b uniformly across its…

Q: A 8-turn generator coil with area 0.155 m^2 rotates in a 1.20 T magnetic field. At what frequency…

Q: The motor in a toy car operates on 5.30 V, developing a 3.90 V back emf at normal speed. If it draws…

Q: You measure the B field at the center of the loop to be zero. What can you say about the current in…

A: If the net field at center is zero, it means the magnetic field due to wire cancels the magnetic…

Q: A teacher wants to build another student a giant solenoid of one layer of tightly-wrapped 12-gauge…

Q: In the figure below, a 30.0 cm x 60.0 cm rectangular circuit containing a 18.102 resistor is…

A: Area of rectangular circuit, A= 0.3×0.6Rate of change in magnetic field.…

Q: Two wires are parallel, with one directly above the other, 9 cm apart. Each wire has a weight per…

A: Distance, d = 9 cm Force per unit length, F = 10-4 N/m

Q: the figure below, the blue wire has a current I = 19 A and the red loop is a square with sides th ce…

Q: Problem 6: In the questions below there are 6 induction processes. The circle with the dot 000000000…

A: According to Lenz's law, the induced electric flows in such a direction that it opposes the change…

Q: R2 Consider the circuit shown in the figure. Suppose that the switch has been open for a very long…

Q: A coil of wire has 400 turns, each of area 50 cm2. What B-field is required if a 4.5 A current…

A: Given data: Number of turns (n) = 400 Area (A) = 50 cm2 = 50×10-4 m2 Current (I) = 4.5 A Maximum…

Q: You want to investigate the voltage, V, induced in a coil due to motion of the magnet. A setup is…

A: Required ; The first step of investigation.

Q: You want to investigate the voltage, V, induced in a coil due to motion of the magnet. A setup is…

Q: Explain the concept of H, B and M (magnetization) in a conductor carrying a current I ! (with…

Q: following transformer circuit VSource=12.0volts, RSource=4, the number of turn on the left-handside…

A: Vs /Vp =Ns / Np

Q: A battery with E = 7.60 V and no internal resistance supplies current to the circuit shown in the…

Q: For the wire arrangement on the right (the square), with currents, directions, and dimensions as…

Q: 1. a. What will be the direction of the current in the wire just above the bar magnet when you…

Q: You want to investigate the voltage, V, induced in a coil due to motion of the magnet. A setup is…

A: Given :

Q: A long solenoid of 80 turns and length 16 cm is known to have a field of 4x10-3 T. What is the…

Q: 4πke ke, B By how much is the approximation B HonI [or in terms of Coulomb's constant -nI] in error…

A: Given,The approximation B = μ0nIThe length of the solenoid, l = 24 cmThe diameter of the solenoid, d…

Concept explainers

Voltage Across Inductor

An actor is a passive electrical component that consists of a coil bent in the form of wire which uses electromagnetism to produce electric current through the coil. When the electric current flows through a conductor that is the coil, a magnetic flux is developed around the conductor. This flow of current through the coil creates a magnetic field based on Fleming's Right-hand thumb rule. If there is any decrease in the current passing through the inductor, then the magnetic field will also decrease and energy is released through the generation of electric current. There is also a secondary voltage inducing in the same coil due to the magnetic flux, since it opposes any changes in the electric current flowing through the circuit. An inductor is also called choke, coil, or solenoid. A choke is designed to block certain frequencies when the DC current passes. A winding coil is coated with insulation to give extra insulation and protect the circuit. They are usually tightly wrapped around a central core which is cylindrical in nature so that the magnetic flux can be induced. The solenoid is a three-dimension coil that is used to exhibit electromagnetism when the magnetic field is developed due to the current flowing through the coil. The sign convention of the inductor is the same as the power dissipating device. When the current flows into the positive side of the voltage across the inductor, the value is positive and the inductor dissipates power whereas when the inductor releases the power back to the circuit, the current has a negative sign convention. 

Question

The figure illustrates the lengthwise cross-section of a current-carrying coil. This coil carries a current \( I \) and contains \( N \) evenly spaced turns along its length \( l \). The illustration presents a portion of this coil with different paths marked as A, B, C, and D.

**Paths and Directions:**

- **Path A:** A rectangular path surrounding a single turn of the coil.
- **Path B:** A rectangular path at the end of the coil, enclosing no current.
- **Path C:** A rectangular path that encircles multiple turns of the coil.
- **Path D:** Another complex path around multiple turns.

**Tasks:**

a. **Evaluate \(\oint \mathbf{B} \cdot d\mathbf{l}\) along path A.**
Give your answer in terms of current \( I \), constant \(\mu_0\), and any numerical constants.
**Additional hint:**
\[
\oint_A \mathbf{B} \cdot d\mathbf{l} = \underline{\hspace{3cm}}
\]
*(Format hint: Spell out Greek letters and use an underscore ("_") for subscripts. For example, to type in \(\mu_0\), type in "mu_0".)*

b. **Evaluate \(\oint \mathbf{B} \cdot d\mathbf{l}\) along path B.**
**Hint for (b):**
\[
\oint_B \mathbf{B} \cdot d\mathbf{l} = \underline{\hspace{3cm}}
\]

c. **Evaluate \(\oint \mathbf{B} \cdot d\mathbf{l}\) along path C.**
**Additional hints for (c) and (d):**
\[
\oint_C \mathbf{B} \cdot d\mathbf{l} = \underline{\hspace{3cm}}
\]

d. **Evaluate \(\oint \mathbf{B} \cdot d\mathbf{l}\) along path D.**
\[
\oint_D \mathbf{B} \cdot d\mathbf{l} = \underline{\hspace{3cm}}
\]

**Explanations:**

- The task involves calculating the line integral of the

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

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.

Similar questions

Please no hand writing solution
I, Iz The picture shows two parallel wires where I1 is 19.6 amps, and I2 is 35.5 amps. The location A is in the plane of the two wires and is 30.0 mm from the left wire and 18.4 mm from the right wire. Given the direction of current in each wire, what is the B-field at the location A in micro teslas? (If the B-field points toward make it positive; if it points away from you, make it negative. Give answer as an integer with correct sign. Do not enter unit.) you,
Force between Parallel Wires You have two wires with current running through them (see image below). The wires are a distance d apart. Current 1 = 3.25 A Current 2 = 2.85 A d = 0.370 m What is the force per length between the wires? Put your answer in μΝ microNewtons/m (· :). m If the force per length is repulsive, put in a negative sign. If the force per length is attractive, leave your answer positive. Your Answer: Answer Wire 1 Current 1 Wire 2 Current 2
The figure below is a cross-sectional view of a coaxial cable. The center conductor is surrounded by a rubber layer, an outer conductor, and another rubber layer. In a particular application, the current in the inner conductor is I, = 1.16 A out of the page and the current in the outer conductor is I, = 2.82 A into the page. Assuming the distance d = 1.00 mm, answer the following. 12 d d (a) Determine the magnitude and direction of the magnetic field at point a. magnitude UT direction ---Select--- (b) Determine the magnitude and direction of the magnetic field at point b. magnitudel UT direction --Select---
A current I flows around the rectangular loop shown in the accompanying figure. B A D Write expressions for B . dl for the paths A, B , C and D A: B: C: D:
The magentic field through a single loop of wire 16.0 cm in radius and of 8.5 ohm resistance changes with time as shown in the figure. Calculate the emf in the loop as a function of time. What is the emf at t=5.0 s? What is the current at t= 1.0 s?
a. b. c. An infinitely long cylinder is placed along the Assume the cylinder z-axis is of radins a and carries current with current density J = 1 az P Find outside the cylinder Find Ĥ inside the cylinder Find in both cases a and b
a L I b L Two long, thin, parallel wires are suspended via 7 cm strings as shown in the Figure above. Each wire has a linear mass density of 55 g/cm. The wires carry identical currents in opposite directions, as shown. a. Use (make a copy) panel b of the Figure above to draw a Free Body Diagram showing the forces acting on one of the wires. b. Find the current in the wires if the system is in equilibrium when the suspending strings make a 6.5 degree angle with respect to the vertical.
A. Find the current in the loop at t = 1.5 s. B. Find the current in the loop at t = 2.5 s.
Connecting arc A wire with current i = 7.2 A is shown. Two semi- infinite straight sections, both tangent to the same circle, are connected by a circular arc that has a central angle and runs along the circumference of the circle. The arc and the two straight sections all lie in the same plane. If B = 0 at the circle's center, what is in rads?
When the resistance of the variable resistor in the lefthand coil is increased at a constant rate, what is the direction of the current in resistor R of the right-hand coil, from a to b or from b to a? Briefly explain.
The figure below shows a cross-sectional view of three parallel wires each carrying a current of 20.0 A. The currents in wires B and C are out of the page while that in wire A is into the page. If the distance R is equal to 4.50 mm, calculate the magnitude of the force (in mN) on wire A (which has a length of 5.60 m) due to the other two wires. Round your answer to 1 decimal place.