Chapter 29: Q23P (page 858)

Figure shows a snapshot of a proton moving at velocity $\vec{v} = (200 \frac{m}{s}) \hat{j}$ toward a long straight wire with current $i = 350 mA$ . At the instant shown, the proton’s distance from the wire is $d = 2.89 cm$ . In unit-vector notation, what is the magnetic force on the proton due to the current?

Short Answer

Expert verified

The magnitude of magnetic force on proton is $(- 7.75 \times 10^{- 23} N) \hat{i}$ .

Step by step solution

Given

Permeability of free space, $μ_{0} = 4 π \times 10^{- 7} \frac{Tm}{A}$ .
Given distance, $d = 2.89 cm$ .
Charge on proton, $q = 1.6 \times 10^{- 19}$ .
Velocity of particle, $v = (- 200 \hat{j})$ .
Current carried by wire, $i = 350 mA$ .

Determine the concept and the formulas:

Calculate the magnetic field due to the long wire at the position of proton. Use this value in the equation of magnetic force to calculate it.

Formula:

Magnetic field

$B = \frac{μ_{0} i}{2 π r}$

Magnetic force, $\vec{F} = q \vec{v} \times \vec{B}$ .

Calculate the magnitude of magnetic force on proton

First of all, we have to find the magnetic field B.

$B = \frac{μ_{0} i}{2 π r}$

$B = \frac{4 π \times 10^{- 7} \times . 350}{2 \times 3.14 \times 2.89 \times 10^{- 2}}$

$B = 2.42 \times 10^{- 6} T$

According to right hand rule, we can say that the magnetic field is out of paper inlocalid="1663227168373" $+ k$ direction.

$B = (2.4221 \times 10^{- 6} T) \hat{k}$

Now, force is

$\vec{F} = q \vec{v} \times \vec{B}$

$\vec{F} = (1.6 \times 10^{- 19}) (- 200 \hat{j}) \times (2.42 \times 10^{- 6} \hat{k})$

localid="1663227211827" $\vec{F} = (- 7.75 \times 10^{- 23} N) \hat{i}$

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Short Answer

Step by step solution

Given

Determine the concept and the formulas:

Calculate the magnitude of magnetic force on proton

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Figure shows a snapshot of a proton moving at velocityv→=200msj^toward a long straight wire with current i=350mA. At the instant shown, the proton’s distance from the wire is d=2.89cm. In unit-vector notation, what is the magnetic force on the proton due to the current?

Short Answer

Step by step solution

Given

Determine the concept and the formulas:

Calculate the magnitude of magnetic force on proton

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Translational Dynamics

Turning Points in Physics

Fields in Physics

Particle Model of Matter

Electricity

Atoms and Radioactivity

Study anywhere. Anytime. Across all devices.