A metal rod of length 20.6 cm and mass 109 g is free to slide over two parallel,

Question

A metal rod of length 20.6 cm and mass 109 g is free to slide over two parallel, horizontal metallic rails connected to a 10.0 V battery (see figure below It is a rectangle with a 10v source on the left side, rod in the middle facing topp to bottom, for some reason it wont let me upload the photo). The battery has internal resistance of 0.100 ?, and the rod and rails have negligible resistance. A 1.86 T magnetic field is directed perpendicular to the plane of the circuit. (a) Find the magnetic force on the rod. magnitude direction ---Select--- into the page out of the page to the right to the left . (b) Find the rod's speed after it has moved 29.7 cm, assuming negligible friction.

Explanation / Answer

Circuit current .. i = E / Rt

10.0V / 0.100

i = 100.0 A

Mag. force F = BiL
F = (1.86T)(100A)(0.206m)

F = 38.31 N
Force direction( Fleming's left-hand rule )
Force direction is along rails away from battery.
b) Rod acceleration

a = F/m = 38.31N / 0.109kg

a = 417 m/s²
Initial vel u = 0
d = 0.297m
v² = u² + 2ad
v² = 0 = (2 x 417m/s² x 0.297m) = 247.69

v = 15.73 m/s

thanks

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