In order to make the rod of Fig. 21–11a move to the right at speed v, you need to apply an external force on the rod to the right. a) Explain and determine the magnitude of the required force. b) What external power is needed to move the rod? (Do not confuse this external force on the rod with the upward force on the electrons shown in Fig. 21–11b.)

Explain and determine the magnitude of the required force.
What external power is needed to move the rod? (Do not confuse this external force on the rod with the upward force on the electrons shown in Fig. 21–11b.)

A conducting rod is moved to the right on a U-shaped conductor in a uniform magnetic field B that points out of the page. The induced current is clockwise.

Figure 21-11 (a) A conducting rod is moved to the right on a U-shaped conductor in a uniform magnetic field

\vec{B}

that points out of the page. The induced current is clockwise.

Upward force on an electron in the metal rod (moving to the right) due to B pointing out of the page; hence electrons can collect at the top of the rod, leaving + charge at the bottom.

Figure 21-11 (b) Upward force on an electron in the metal rod (moving to the right) due to

\vec{B}

pointing out of the page; hence electrons can collect at the top of the rod, leaving + charge at the bottom.

$\dfrac{B^2l^2v}{R}$
$\dfrac{B^2l^2v^2}{R}$

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In order to make the rod of Fig. 21–11a move to the right at speed vvv, you need to apply an external force on the rod to the right.

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In order to make the rod of Fig. 21–11a move to the right at speed $v$ , you need to apply an external force on the rod to the right.