Table of contents

0. Math Review31m
- Math Review
  31m
1. Intro to Physics Units1h 29m
2. 1D Motion / Kinematics3h 56m
3. Vectors2h 43m
4. 2D Kinematics1h 42m
5. Projectile Motion3h 6m
6. Intro to Forces (Dynamics)3h 22m
7. Friction, Inclines, Systems2h 44m
8. Centripetal Forces & Gravitation7h 26m
9. Work & Energy1h 59m
10. Conservation of Energy2h 54m
11. Momentum & Impulse3h 40m
12. Rotational Kinematics2h 59m
13. Rotational Inertia & Energy7h 4m
14. Torque & Rotational Dynamics2h 5m
15. Rotational Equilibrium3h 39m
16. Angular Momentum3h 6m
17. Periodic Motion2h 9m
18. Waves & Sound3h 40m
19. Fluid Mechanics4h 27m
20. Heat and Temperature3h 7m
21. Kinetic Theory of Ideal Gases1h 50m
22. The First Law of Thermodynamics1h 26m
23. The Second Law of Thermodynamics3h 11m
24. Electric Force & Field; Gauss' Law3h 42m
25. Electric Potential1h 51m
26. Capacitors & Dielectrics2h 2m
27. Resistors & DC Circuits3h 8m
28. Magnetic Fields and Forces2h 23m
29. Sources of Magnetic Field2h 30m
30. Induction and Inductance3h 38m
31. Alternating Current2h 37m
32. Electromagnetic Waves2h 14m
33. Geometric Optics2h 57m
34. Wave Optics1h 15m
35. Special Relativity2h 10m

28. Magnetic Fields and Forces

Magnetic Force on Current-Carrying Wire

Physics

28. Magnetic Fields and Forces

Magnetic Force on Current-Carrying Wire

Previous problemNext problem

5:22 minutes

Problem 78

Textbook Question

A small but rigid U-shaped wire carrying a 5.0-A current (Fig. 28–67) is placed inside a solenoid. The solenoid is 15.0 cm long and has 600 loops of wire, and the current in each loop is 7.0 A. What is the net force on the U-shaped wire?

Verified step by step guidance

Step 1: Calculate the magnetic field inside the solenoid using the formula for the magnetic field of a solenoid:

B = μ

₀nI, where

μ

₀ is the permeability of free space (

4 π \times 10 ⁻ 7

T·m/A),

n

is the number of turns per unit length (

600 / 0.15

turns/m), and

I

is the current in the solenoid (

7.0

A).

Step 2: Determine the force on each segment of the U-shaped wire using the formula for the magnetic force on a current-carrying wire:

F = I L B \sin (θ)

, where

I

is the current in the wire (

5.0

A),

L

is the length of the wire segment,

B

is the magnetic field calculated in Step 1, and

θ

is the angle between the wire and the magnetic field.

Step 3: Analyze the forces on the vertical segments of the U-shaped wire. Since the magnetic field is perpendicular to these segments (

θ = 90 °

), the force will be maximized. Use the formula from Step 2 to calculate the force on each vertical segment, considering their lengths (

1.25

cm).

Step 4: Analyze the force on the horizontal segment of the U-shaped wire. Since the magnetic field is parallel to this segment (

θ = 0 °

), the force will be zero because

\sin (0) = 0

Step 5: Sum the forces on the vertical segments. Since the forces on the two vertical segments are equal in magnitude but opposite in direction, the net force on the U-shaped wire will be the vector sum of these forces. Consider the direction of the forces to determine the net force.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Play a video:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Magnetic Field in a Solenoid

A solenoid generates a uniform magnetic field inside it when an electric current flows through its coils. The strength of this magnetic field (B) can be calculated using the formula B = μ₀ * (N/L) * I, where μ₀ is the permeability of free space, N is the number of loops, L is the length of the solenoid, and I is the current. In this case, understanding the magnetic field produced by the solenoid is crucial for determining the force on the U-shaped wire.

Lorentz Force

The Lorentz force describes the force experienced by a charged particle moving through a magnetic field. For a current-carrying conductor, the force (F) can be calculated using F = I * L × B, where I is the current, L is the length vector of the conductor, and B is the magnetic field vector. This concept is essential for calculating the net force acting on the U-shaped wire due to the magnetic field of the solenoid.

Direction of Force (Right-Hand Rule)

The direction of the force on a current-carrying conductor in a magnetic field can be determined using the right-hand rule. By pointing the thumb of the right hand in the direction of the current and the fingers in the direction of the magnetic field, the palm will face the direction of the force. This rule is vital for understanding how the U-shaped wire will interact with the magnetic field created by the solenoid.

Watch next

Master Magnetic Force on Current-Carrying Wire with a bite sized video explanation from Patrick

Start learning

Related Videos

Related Practice

Textbook Question

In FIGURE P29.75, a long, straight, current-carrying wire of linear mass density μ is suspended by threads. A magnetic field perpendicular to the wire exerts a horizontal force that deflects the wire to an equilibrium angle θ. Find an expression for the strength and direction of the magnetic field B.

152

views

Textbook Question

The two 10-cm-long parallel wires in FIGURE EX29.33 are separated by 5.0 mm. For what value of the resistor R will the force between the two wires be 5.4 x 10⁻⁵ N?

A wire along the x-axis carries current I in the negative x-direction through the magnetic field $\vec{B} = {\begin{matrix} B_{0} \frac{x}{l} \hat{k} & 0 \leq x \leq l \\ 0 & elsewhere \end{matrix}$ . Find an expression for the net torque on the wire about the point x = 0.

139

views

Textbook Question

FIGURE EX29.37 is a cross section through three long wires with linear mass density 50 g/m. They each carry equal currents in the directions shown. The lower two wires are 4.0 cm apart and are attached to a table. What current I will allow the upper wire to 'float' so as to form an equilateral triangle with the lower wires?

1157

views

Textbook Question

(a) What is the force per meter of length on a straight wire carrying a 7.40-A current when perpendicular to a 0.90-T uniform magnetic field?

(b) What if the angle between the wire and field is 35.0°?

759

views

Textbook Question

The magnetic force per meter on a wire is measured to be only 55% of its maximum possible value. What is the angle between the wire and the magnetic field?

465

views

Textbook Question

A bolt of lightning strikes a metal flag pole, one end of which is anchored in the ground. Estimate the force the Earth’s magnetic field can exert on the flag pole while the lightning-induced current flows. See Example 25–10.

217

views

Textbook Question

Near the equator, the Earth’s magnetic field points almost horizontally to the north and has magnitude B = 0.50 x 10⁻⁴ T. What should be the magnitude and direction for the velocity of an electron if its weight is to be exactly balanced by the magnetic force?

201

views

Show more practices

Download the Mobile app

Privacy

Do not sell my personal information

Accessibility

Patent notice

Sitemap