a long wire at x=-5 meters and z=0 stretching from y=infinity to y= negative inf

Question

a long wire at x=-5 meters and z=0 stretching from y=infinity to y= negative infinity carries a current of 23 A in the y direction.

a) determine the magnetic field (magnitude and direction) from the long wire at the location (2,3,0). A proton at the location (2,3,0) is moving with the speed of 7.1 E6 m/s in the x direction.

b) determine the magnetic force ( magnitude and direction) on the proton.

c) could you use your results, newtons second law, and kinematics equations from the text to predict subsequent motion of the proton?

Explanation / Answer

The magnetic field due to an infinite wire is given as: B = µoI/2R where R is the distance from the wire.

Part a.) The magnetic field due to the wire at x = -5m would be given as:

B = 2 x 10-7 x 23 / 7 = 6.57 x 10-7 T

Therefore the magnetic field at 2,3,0 is 6.57 x 10-7 T and it will be along negative z direction.

Part b.) The force acting on a charge q moving with velcoity v in the magnetic field B is given as:

F= q V x B and the direction of the force is given as the cross product of the velocity and the magnetic field.

So the force on the proton would be given as: 1.60217662 × 10-19 x 7.1 x e6 x 6.57 x 10-7

or, F = 3.02654 x 10-16 N and the direction of the force will be along the Y direction as the proton is moving in the x and the magnetic field is along the negative z

Part c.) For the given we can say that the proton will suffer a force towards the Y axis as determined above, and will start accelerating towards y direction.

However the particle will have no acceleration along the x direction and will continue to have the same velocity component along the x axis. Therefore the proton will start to go about a curved path.

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