First slide

Energy consideration quantitative study.

Question

A rectangular loop with a sliding connector of length l = 1.0 m is situated in a uniform magnetic field B = 2T perpendicular to the plane of loop. Resistance of connector is r = 2 $Ω$ . Two resistance of 6 $Ω$ and 3 $Ω$ are connected as shown in figure. The external force required to keep the connector moving with a constant velocity v = 2m/s is

Moderate

A

6 N
B

4 N
C

2 N
D

1 N

Solution

Motional emf $e = B v l \Rightarrow e = 2 \times 2 \times 1 = 4 V$
This acts as a cell of emf E = 4 V and internal resistance $r = 2 Ω$ .
This simple circuit can be drawn as follows

Current through the connector $i = \frac{4}{2 + 2} = 1 A$
$∴$ magnetic force on connector $F_{m} = B i l = 2 \times 1 \times 1 = 2 N$
(Towards left) A force of 2N has to be applied towards right.

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