Shows a rod PQ of length 20.0 cm and mass 200g suspended through a fixed point O by two threads of lengths 20.0 cm each. A magnetic field of strenght 0.500 T exists in the vicinity of the wire PQ as shown in the figure. The exists in the vicinity of the wire PQ as shown in the figure. The wires conecting 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.

Explanation

(a) When switch `S` is open

`2T sin 60^(@) = mg`
`T = (mg)/(sqrt(3)) = (200 xx 10^(-3) xx 10)/(sqrt(3))`
`= (2)/(sqrt(3))N`
(b) When switch `S` is closed, current `i` is in wire `PQ`. Magnetic force on `PQ`, `F_(m) = Bil`, downward

`2T' sin 60^(@) = mg + Bil`
`T' = (mg + Bil)/(sqrt(3))`
`= (200 xx 10^(-3) xx 10 + 0.5 xx 2 xx 0.2)/(sqrt(3))`
`= 2 + (0.2)/(sqrt(3)) = (2.2)/(sqrt(3))N`