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A loop of wire in the shape of a rectangle of width w and length L and a long, straight wire carrying a current I lie on a tabletop as shown in the figure below. (a) Determine the magnetic flux through the loop due to the current I. (Use any variable stated above along with the following as necessary: Ho-) (b) Suppose the current is changing with time according to I = a + bt, where a and b are constants. Determine the magnitude of the emf (in V) that is induced in the loop if b = 16.0 A/s, h = 1.00 cm, w = 20.0 cm, and L = 1.35 m. (c) What is the direction of the induced current in the rectangle? clockwise counterclockwise The magnitude is zero.

A loop of wire in the shape of a rectangle of width w and length L and a long, straight wire carrying a current I lie on a tabletop as shown in the figure below. (a) Determine the magnetic flux through the loop due to the current I. (Use any variable stated above along with the following as necessary: Ho-) (b) Suppose the current is changing with time according to I = a + bt, where a and b are constants. Determine the magnitude of the emf (in V) that is induced in the loop if b = 16.0 A/s, h = 1.00 cm, w = 20.0 cm, and L = 1.35 m. (c) What is the direction of the induced current in the rectangle? clockwise counterclockwise The magnitude is zero.

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**Magnetic Flux and Induced EMF in a Rectangular Loop** In this exercise, we analyze a rectangular loop of wire with width \( w \) and length \( L \), and a long, straight wire carrying a current \( I \) lying on a tabletop as illustrated in the figure. ### Diagram Description The diagram illustrates a rectangular loop of width \( w \) and length \( L \), placed near a straight wire carrying a current \( I \). The straight wire is positioned parallel to one of the lengths of the rectangle, separated by a distance \( h \). ### Problem Analysis **(a) Determine the magnetic flux through the loop due to the current \( I \). (Use any variable stated above along with the following as necessary: \(\mu_0\).)** \[ \Phi_B = \] ______ **(b) Suppose the current is changing with time according to \( I = a + bt \), where \( a \) and \( b \) are constants. Determine the magnitude of the emf (in V) that is induced in the loop if \( b = 16.0 \, \text{A/s} \), \( h = 1.00 \, \text{cm} \), \( w = 20.0 \, \text{cm} \), and \( L = 1.35 \, \text{m} \).** \[ \text{EMF} = \] ______ V **(c) What is the direction of the induced current in the rectangle?** - ⃝ Clockwise - ⃝ Counterclockwise - ⃝ The magnitude is zero. **What If?** Suppose a constant current \( I = 6.00 \, \text{A} \) flows in the straight wire and the loop moves from an initial position \( h_0 = 1.00 \, \text{cm} \) toward the bottom of the figure at a constant speed of \( v = 18.0 \, \text{cm/s} \). **(d) What is the magnitude of the induced emf (in V) in the loop 1.00 s after it begins to move?** \[ \text{EMF} = \] ______ V **(e) What is the direction of the induced current in the loop 1.00 s after it begins to move?** -
Transcribed Image Text:**Magnetic Flux and Induced EMF in a Rectangular Loop** In this exercise, we analyze a rectangular loop of wire with width \( w \) and length \( L \), and a long, straight wire carrying a current \( I \) lying on a tabletop as illustrated in the figure. ### Diagram Description The diagram illustrates a rectangular loop of width \( w \) and length \( L \), placed near a straight wire carrying a current \( I \). The straight wire is positioned parallel to one of the lengths of the rectangle, separated by a distance \( h \). ### Problem Analysis **(a) Determine the magnetic flux through the loop due to the current \( I \). (Use any variable stated above along with the following as necessary: \(\mu_0\).)** \[ \Phi_B = \] ______ **(b) Suppose the current is changing with time according to \( I = a + bt \), where \( a \) and \( b \) are constants. Determine the magnitude of the emf (in V) that is induced in the loop if \( b = 16.0 \, \text{A/s} \), \( h = 1.00 \, \text{cm} \), \( w = 20.0 \, \text{cm} \), and \( L = 1.35 \, \text{m} \).** \[ \text{EMF} = \] ______ V **(c) What is the direction of the induced current in the rectangle?** - ⃝ Clockwise - ⃝ Counterclockwise - ⃝ The magnitude is zero. **What If?** Suppose a constant current \( I = 6.00 \, \text{A} \) flows in the straight wire and the loop moves from an initial position \( h_0 = 1.00 \, \text{cm} \) toward the bottom of the figure at a constant speed of \( v = 18.0 \, \text{cm/s} \). **(d) What is the magnitude of the induced emf (in V) in the loop 1.00 s after it begins to move?** \[ \text{EMF} = \] ______ V **(e) What is the direction of the induced current in the loop 1.00 s after it begins to move?** -
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