Chapter 28: Q14P (page 829)

A metal strip6.50cm long, 0.850 cm wide, and 0.760 mm thick moves with constant velocity through a uniform magnetic field B=1.20mT directed perpendicular to the strip, as shown in Fig.12-34. A potential difference of 3.90 $μ v$ is measured between points xand yacross the strip. Calculate the speed.

Short Answer

Expert verified

The speed of the metal strip is $v = 3.9 μ V (\frac{10^{- 8}}{1 μ v}) = 3.9 \times 10^{- 6} v$ v=0.382 m/s .

Step by step solution

Given

$V = 3.9 μV (\frac{10^{- 6} V}{1 μV}) = 3. 9 \times 10^{-6} V$

$d = 0.850 cm (\frac{10^{- 2} m}{1 cm}) = 8.50 \times 10^{-3} m$

$B = 1 .20 mT (\frac{10^{-3} T}{1 mT}) = 1.20 \times 10^{-3} T$

Determining the concept

If the strip is moving with constant velocity, then acceleration will be zero. So electric and magnetic forces will balance each other

Formulae are as follows:

$F_{e} = q E$

$F_{m} = q v B$

$E = V/d$

Where F_eis electric force, F_m is a magnetic force,

v is velocity, E is the electric field, B is the magnetic field, q is the charge of the particle, and d is distance.

Determining the speed of the metal strip

Here, both forces are in balance.

Hence,

$F_{m} = F_{e}$

$qvB = qE$

$v = \frac{E}{B}$

$v = \frac{V}{Bd}$

$\begin{matrix} v = \frac{3.9 \times 10^{- 6} V}{1.20 \times 10^{- 3} T \times 8.50 \times 10^{- 3} m} \\ = 0.382 m / s \end{matrix}$

Hence, the speed of the metal strip is, $v = 0.382m/s$ .

Therefore, by using the formula of electric and magnetic forces, the velocity of the metal strip can be determined.

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A metal strip6.50cm long, 0.850 cm wide, and 0.760 mm thick moves with constant velocity through a uniform magnetic field B=1.20mT directed perpendicular to the strip, as shown in Fig.12-34. A potential difference of 3.90 $μ v$ is measured between points xand yacross the strip. Calculate the speed.

Short Answer

Step by step solution

Given

Determining the concept

Determining the speed of the metal strip

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A metal strip6.50cm long, 0.850 cm wide, and 0.760 mm thick moves with constant velocity through a uniform magnetic field B=1.20mT directed perpendicular to the strip, as shown in Fig.12-34. A potential difference of 3.90μvis measured between points xand yacross the strip. Calculate the speed.

Short Answer

Step by step solution

Given

Determining the concept

Determining the speed of the metal strip

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Physical Quantities And Units

Radiation

Mechanics and Materials

Engineering Physics

Energy Physics

Thermodynamics

Study anywhere. Anytime. Across all devices.