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Question

In Figure , a metal rod is forced to move with constant velocity $$\overrightarrow {v}$$ along two parallel metal rails, connected with a strip of metal at one end. A magnetic field of magnitude B = 0.350 T points out of the page.

(a) If the rails are separated by L = 25.0 cm and the speed of the rod is 55.0 cm/s, what emf is generated?

(b) If the rod has a resistance of $$18.0\Omega $$ and the rails and connector have negligible resistance, what is the current in the rod?
(c) At what rate is energy being transferred to thermal energy?



Solution
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(a) Equation $$\mathscr{E}=\dfrac{d\Phi
_B}{dt}=\dfrac{d}{dt}BLx=BL\dfrac{dx}{dt}=BLv$$ leads to

$$\varepsilon=B L v=(0.350
\mathrm{T})(0.250 \mathrm{m})(0.55 \mathrm{m} / \mathrm{s})=0.0481 \mathrm{V}$$

(b) By Ohm's law, the induced current is

$$i=0.0481 \mathrm{V} / 18.0
\Omega=0.00267 \mathrm{A}$$

By Lenz's law, the current is clockwise in Figure.

(c) Equation $$P=i^2R\text{ (resistive dissipation) }$$ leads to $$P=i^{2}
R=0.000129 \mathrm{W}$$

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Similar Questions
Q1

In Figure , a metal rod is forced to move with constant velocity $$\overrightarrow {v}$$ along two parallel metal rails, connected with a strip of metal at one end. A magnetic field of magnitude B = 0.350 T points out of the page.

(a) If the rails are separated by L = 25.0 cm and the speed of the rod is 55.0 cm/s, what emf is generated?

(b) If the rod has a resistance of $$18.0\Omega $$ and the rails and connector have negligible resistance, what is the current in the rod?
(c) At what rate is energy being transferred to thermal energy?



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Q2
The conducting rod shown in Figure has length L and is being pulled along horizontal, frictionless conducting rails at a constant velocity $$\overrightarrow {v}$$. The rails are connected at one end with a metal strip. A uniform magnetic field $$\overrightarrow {B}$$, directed out of the page, fills the region in which the rod moves. Assume that L = 10 cm, v = 5.0 m/s, and B = 1.2 T. What are the (a) magnitude and (b) direction (up or down the page) of the emf induced in the rod? What are the (c) size and (d) direction of the current in the conducting loop? Assume that the resistance of the rod is $$0.40\Omega $$ and that the resistance of the rails and metal strip is negligibly small. (e) At what rate is thermal energy being generated in the rod? (f) What external force on the rod is needed to maintain $$\overrightarrow {v}$$ ? (g) At what rate does this force do work on the rod?

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Q3

Figure shows a rod of length L =10.0 cm that is forced to move at constant speed v =5.00m/s along horizontal rails. The rod, rails, and connecting strip at the right form a conducting loop. The rod has resistance $$0.400\Omega $$; the rest of the loop has negligible resistance. A current $$i=100A$$ through the long straight wire at distance a = 10.0 mm from the loop sets up a (nonuniform) magnetic field through the loop. Find the a) emf and (b) current induced in the loop. (c) At what rate is thermal energy generated in the rod? (d) What is the magnitude of the force that must be applied to the rod to make it move at constant speed? (e) At what rate does this force do work on the rod?



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Q4
Lenz's Law (37)
Two parallel rails with negligible resistance are $$10.0 \,cm$$ apart and are connected by a resistor of resistance $$R_3= 5.00 \Omega$$. The circuit also contains two metal rods having resistances of $$R_1 = 10.0 \Omega$$ and $$R_2 = 15.0 \,\Omega$$ sliding along the rails (Figure). The rods are pulled away from the resistor at constant speeds of $$v_1 = 4.00 \,m/s$$ and $$v_2 = 2.00 \,m/s$$, respectively. A uniform magnetic field of magnitude $$B = 0.010 0 \,T$$ is applied perpendicular to the plane of the rails. Determine the current in $$R_3$$.

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Q5

Consider two parallel conducting rails placed in a uniform magnetic field as shown in figure. The rails and the rod PQ are having negligible resistance of 100Ω. The rod is moving towards right with constant velocity of v=5ms-1.The magnitude of magnetic field is 2T and l=0.2m.

Based on the above information, answer the following questions.

The emf induced by the moving rod is


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