A current carrying conductor in an outside magnetic field experiences a force. R
ID: 1323355 • Letter: A
Question
A current carrying conductor in an outside magnetic field experiences a force. Rail guns use this force to launch projectiles. A simple model of a rail gun consists of a conducting bar (of mass m and square in cross section with sides x) carrying a current I (supplied by the rails) that is free to slide on a pair of parallel rails a distance L apart. The bar is perpendicular to the rails and is initially at rest. An object can be mounted on the bar and it can be accelerated together with the bar.
A) What orientation should a uniform external magnetic field B have in order to move the bar along the rails to the right?
B) What is the force on the bar as a function of this magnetic field and the current?
C) What is the minimum rail length required to accelerate the bar to a velocity v?
D) What assumptions do you need to make? Name at least 2.
E) Would this be a reasonable way to launch a satellite? Assume the satellite has a mass of 100kg, the field is 2T, the rails are 1m apart and the current is 100A. Assume the satellite needs to acquire escape velocity.
A current carrying conductor in an outside magnetic field experiences a force. Rail guns use this force to launch projectiles. A simple model of a rail gun consists of a conducting bar (of mass m and square in cross section with sides x) carrying a current I (supplied by the rails) that is free to slide on a pair of parallel rails a distance L apart. The bar is perpendicular to the rails and is initially at rest. An object can be mounted on the bar and it can be accelerated together with the bar. A) What orientation should a uniform external magnetic field B have in order to move the bar along the rails to the right? B) What is the force on the bar as a function of this magnetic field and the current? C) What is the minimum rail length required to accelerate the bar to a velocity v? D) What assumptions do you need to make? Name at least 2. E) Would this be a reasonable way to launch a satellite? Assume the satellite has a mass of 100kg, the field is 2T, the rails are 1m apart and the current is 100A. Assume the satellite needs to acquire escape velocity.Explanation / Answer
A) The orientation of uniform external magnetic field B should be upward in order to move the bar along rails to the right.
B) F= ILB, here L is the length of the bar.
C) Acceleration, a= ILB/m
Using equation of motion,
v^2=u^2+2as
s= v^2/2a= v^2/ 2ILB/m= mv^2/2ILB
D.) The assumption would be that the friction between rail and bar is zero and air resistance is also zero.
E). Escape velocity V=11.6 Km/s= 1.16*10^4 m/s.
Plugging the values in length of rail, s= (1.16*10^4)^2*100/2*1*100=6.7*10^7 m. So, rail has to be very long. So, it is not reasonable.