Question

Figure (34 - E7) shows a rod PQ of length 20.0 cm and mass 200 g suspended through a fixed point O by two threads of lengths 20.0 cm each. A magnetic field of strength 0.500 T exists in the vicinity of the wire PQ as shown in the figure. The wires connecting PQ with the battery are loose and exert no force on PQ. (a) Find the tension in the threads when the switch S is open. (b) A current of 2.0 A is established when the switch S is closed. Find the tension in the threads now.

Answer 1

(a) When switch S is open

2T cos ${30}^o$ = mg

$\Rightarrow T=mg/2cos{30}^o$

$=\frac{2}{\sqrt{3}}$= 1.13 N.

(b) When the switch is closed and a current passed through the circuit = 2A.

Then, 2T cos ${30}^o$

$=mg+ilB$

$=200\times {10}^{-s}\times 9.8+2\times 0.2\times 0.5$

$=1.95+0.2=2.16$

$\Rightarrow 2T=2.49$

T = 1.245 = 1.25 N.