Chapter 29: Q21P (page 858)

Figure 29-49 shows two very long straight wires (in cross section) that each carry a current of $4.00 A$ directly out of the page. Distance $d_{1} = 6.00 m$ and distance $d_{2} = 4.00 m$ . What is the magnitude of the net magnetic field at point P, which lies on a perpendicular bisector to the wires?

Short Answer

Expert verified

Magnitude of the net magnetic field at point P is $256 nT$ .

Step by step solution

Given

Permeability of free space, $μ_{0} = 4 π \times 10^{- 7} \frac{Tm}{A}$ .
$d_{1} = 6.00 m$ .
$d_{2} = 4.00 m$ .
Current carried by wire, $i = 4.00 A$ .

Understanding the concept

By using the concept of magnetic field due to long wire carrying current and component of magnetic field, determine the net magnetic field at point P.

Formula:

Magnetic field due to the wire at point P is

$B = \frac{μ_{0} i}{2 π r}$

Here, $i = current$ , $μ_{0} =$ permeability of free space, $r =$ distance of wire.

Calculate the magnitude of the net magnetic field at point P.

First of all, we have to find the r.

By using Pythagoras theorem, solve as:

$r = \sqrt{{(\frac{d_{1}}{2})}^{2} + {(d_{2})}^{2}}$

$r = \sqrt{{(\frac{6}{2})}^{2} + {(4)}^{2}}$

$r = \sqrt{25} r = 5.00 m$

Now, the magnetic field is given by

$B = \frac{μ_{0} i}{2 π r}$

$B = \frac{4 π \times 10^{- 7} \times 4.0}{2 \times 3.14 \times 5.00}$

$B = 1.6 \times 10^{- 7} T$

$B = 160 nT$

The component of the magnetic field cancels with each other, so the magnetic field at point P is

$B_{p} = 2 B s i n θ$

Here,

$s i n θ = \frac{d_{2}}{r} = \frac{4.00}{5.00} = 0.8$

$B_{p} = 2 \times 160 \times 0.8$

$B_{p} = 256 nT$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Short Answer

Step by step solution

Given

Understanding the concept

Calculate the magnitude of the net magnetic field at point P.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Mechanics and Materials

Magnetism

Physical Quantities And Units

Astrophysics

Rotational Dynamics

Medical Physics

Study anywhere. Anytime. Across all devices.

Figure 29-49 shows two very long straight wires (in cross section) that each carry a current of4.00A directly out of the page. Distance d1=6.00m and distance d2=4.00m. What is the magnitude of the net magnetic field at point P, which lies on a perpendicular bisector to the wires?

Short Answer

Step by step solution

Given

Understanding the concept

Calculate the magnitude of the net magnetic field at point P.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Mechanics and Materials

Magnetism

Physical Quantities And Units

Astrophysics

Rotational Dynamics

Medical Physics

Study anywhere. Anytime. Across all devices.