c).Show thus that the magnetic force exerted on the unit length of payload, can bewritten asHọ iD|dx| 1(D? -x?)dF(x)(2)d,. As you can see right away, B(x) turns out to be infinite at x = -D and x = D. Howcoie that a finite current can produce an infinite magnetic force? (What is inadmissible inthe derivation of the above expression?)We overlook the foregoing problem, and we propose to calculate dF(x)/dx], at x=0.What should be i, if we wish to obtain a force per unit length, just to overcome Earth'sacceleration, g=10 m/s?, for a payload of mass m=200 kg, given that D = 1 m? Hint: Findthe weight per unit length (mg/2D) and equate it to the right hand side of Eq.(2). You willsee that i, is huge, and this is why this technique is not appropriate to launch anything tospace, from Earth. Question 2The rail gun is an electric device, conceived to launch a payload, installed on a rail systemcomposed of two parallel rails. Suppose you are located at the origin of the rails, and you lookahead. A large electric current is sent along the left hand side (LHS) rail. A conducting fuseelement placed below the payload and in between the rails, conveys the current across, andthen back, along the right hand side (RHS) rail. The electric current sent in, produces amagnetic field below the payload, and, the same current flowing through the magnetic field,becomes subject to an upward magnetic force. The distance in between the rails is 2D.Consider a two dimensional coordinate system (yOx): Let the Oy direction, the direction ofmotion of the projectile through the launch, along the rails, and the Ox direction, the directionperpendicular to Oy. Place the origin, in the middle of the rails, behind the payload.Following the passage of the current of intensity i, the fuse element melts and vaporizes,creating a gas, but still bearing the capability of conducting the electric current across therails, along the back side of the payload. The conducting gas, propels the projectile all alongthe rails, and finally brings it to the stage of launch.a) Show that the net magnetic fieldintensity B(x) at x, created by both the LHS and theRHS rail current, can be calculated to beHo iDB(x) :(1)a(D? - x)Precise the direction of the magnetic field vector B(x), and sketch B(x) versus x. Note thatthe permeability constant, in MKS unit system, is u,=4n x 10-7.Based (with the familiar notation), on the infinitely small magnetic force dF, exertedon an infinitely small charge dq, moving with the velocity v, i.e. dF=v dq x B, show thatthe magnitude dF(x), of the force exerted on the infinitely small piece of payload of width|dx], around the location |x|, can be expressed as dF(x)= idx| B(x).

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(Based (1with the familiar notation), on the infinitely small magnetic force dF, exerted on an infinitely small charge dq, moving with the velocity v, i.e. dF v dq x B, show that the magnitude dF(x), of the force exerted on the infinitely small piece of payload of width |dx], around the location |x, can be expressed as dF(x)= idx| B(x).

(Based (1with the familiar notation), on the infinitely small magnetic force dF, exerted on an infinitely small charge dq, moving with the velocity v, i.e. dF v dq x B, show that the magnitude dF(x), of the force exerted on the infinitely small piece of payload of width |dx], around the location |x, can be expressed as dF(x)= idx| B(x).