Chapter 30: Q. 37 (page 871)

A $20 cm \times 20 cm$ square loop has a resistance of $0.10 Ω$ . A CALC magnetic field perpendicular to the loop is $B = 4 t - 2 t^{2}$ , where $B$ is in Tesla and $t$ is in seconds. What is the current in the loop at $t = 0.0 s, t = 1.0 s$ ,and $t = 2.0 s ?$

Short Answer

Expert verified

Current in the loop at $I_{0 s}$ is $1.6 A$ .

Current in the loop at $I_{1 s}$ is $0 A$ .

Current in the loop at $I_{2 s}$ is $- 1.6 A$ .

Step by step solution

Formula for electric flux inside the loop

The magnetic field is expressed in terms of time in the form

$B = 4 t - 2 t^{2}$

The loop's current state is,

$I_{induced} = \frac{ε}{R}$

$ε = |\frac{{dΦ}_{m}}{dt}|$

The electric flow as a function of area is,

$Φ_{m} = NBA$

So,

$ε = NA \frac{d (BA)}{dt} = NA \frac{dB}{dt}$

Calculation for current in the loop att=0.0 s

Current that has been induced is,

$I_{induced} = (\frac{NA}{R}) \frac{dB}{dt}$

$= (\frac{NA}{R}) \frac{d}{dt} (4 t - 2 t^{2})$

$= (\frac{NA}{R}) (4 - 4 t)$

The area of the loop is calculated using

$A = 0.20 m \times 0.20 m = 4 \times 10^{- 2} m^{2}$

At $t = 0.0 s$ :

Induced current is,

$I_{0 s} = (\frac{NA}{R}) (4 - 4 t)$

$= (\frac{(1) (4 \times 10^{- 2} m^{2})}{0.10 Ω}) (4 - 4 (0 s))$

$= 1.6 A$

Calculation for current in the loop at t=1.0 s and t=2.0 s

At $t = 1.0 s$ :

Induced current is,

$I_{1 s} = (\frac{NA}{R}) (4 - 4 t)$

$= (\frac{(1) (4 \times 10^{- 2} m^{2})}{0.10 Ω}) (4 - 4 (1 s))$

$= 0 A$

At $t = 2.0 s$ :

Induced current is,

$I_{2 s} = (\frac{NA}{R}) (4 - 4 t)$

$= (\frac{(1) (4 \times 10^{- 2} m^{2})}{0.10 Ω}) (4 - 4 (2 s))$

$- 1.6 A$ $= (\frac{(1) (4 \times 10^{- 2} m^{2})}{0.10 Ω}) (4 - 4 (1 s))$

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A $20 cm \times 20 cm$ square loop has a resistance of $0.10 Ω$ . A CALC magnetic field perpendicular to the loop is $B = 4 t - 2 t^{2}$ , where $B$ is in Tesla and $t$ is in seconds. What is the current in the loop at $t = 0.0 s, t = 1.0 s$ ,and $t = 2.0 s ?$

Short Answer

Step by step solution

Formula for electric flux inside the loop

Calculation for current in the loop att=0.0 s

Calculation for current in the loop at t=1.0 s and t=2.0 s

One App. One Place for Learning.

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A 20cm×20cmsquare loop has a resistance of 0.10Ω. A CALC magnetic field perpendicular to the loop is B=4t-2t2, where Bis in Tesla andtis in seconds. What is the current in the loop at t=0.0s,t=1.0s,andt=2.0s?

Short Answer

Step by step solution

Formula for electric flux inside the loop

Calculation for current in the loop att=0.0 s

Calculation for current in the loop at t=1.0 s and t=2.0 s

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Measurements

Modern Physics

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Fluids

Study anywhere. Anytime. Across all devices.

A $20 cm \times 20 cm$ square loop has a resistance of $0.10 Ω$ . A CALC magnetic field perpendicular to the loop is $B = 4 t - 2 t^{2}$ , where $B$ is in Tesla and $t$ is in seconds. What is the current in the loop at $t = 0.0 s, t = 1.0 s$ ,and $t = 2.0 s ?$