A metal rod of length 22.0 cm and mass 108 g is free to slide over two parallel,

Question

A metal rod of length 22.0 cm and mass 108 g is free to slide over two parallel, horizontal metallic rails connected to a 10.0 V battery (see figure below). The battery has internal resistance of 0.100 , and the rod and rails have negligible resistance. A 1.98 T magnetic field is directed perpendicular to the plane of the circuit.

(a) Find the magnetic force on the rod.

(b) Find the rod's speed after it has moved 28.5 cm, assuming negligible friction.

Explanation / Answer

Circuit current .. i = E / R=10.0V / 0.10 i = 100.0A
Mag. force ..F = BiL
F = (1.98T)(100A)(0.22m)

F = 43.56N

Force direction obtained by applying Fleming's left-hand rule ..

Force direction is along rails away from battery.

b)
Rod acceleration is

a = F/m = 43.56N / 0.108kg .

a = 402.3 m/s²
Initial vel u = 0
d = 0.285m
v² = u² + 2ad

v² = 0 +(2 x 402.3m/s² x 0.285m)

v = 15.14 m/s

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