Please show the integration required for the problem and in the desired units. Thank you!!!
voltage generated due to rod of lenght l moving with a velocity v
in a magnetic field
from free body diagram of rod,
force on the rod with current i and length l= ilB.
m(dv/dt)= mgsinθ - i lB;
i= (vBl)/R;
m(dv/dt) = mgsinθ - (vB2l2)/R,
let B2l2 /Rm=k,
then,
dv/dt + kv=gsinθ,
integrating factor = ekt.
solving this differential equation we get,
ekt v=(gsinθ/k)ekt -(gsinθ)/k
hence
v= [(gsinθ)/k](1-e-kt). ans.
Please show the integration required for the problem and in the desired units. Thank you!!! A...
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