A long, rigid conductor, lying along the x axis, carries acurrent of 5.5 A in th

Question

A long, rigid conductor, lying along the x axis, carries acurrent of 5.5 A in the negative direction. A magneticfield B is present, given by B =4.0i + 6.0x2j , withx in meters and B in m T.

1. Calculate the k-component of the force onthe 2 m segment of the conductor that lies between x = 1.0m and x = 3.0 m. A long, rigid conductor, lying along the x axis, carries acurrent of 5.5 A in the negative direction. A magneticfield B is present, given by B =4.0i + 6.0x2j , withx in meters and B in m T.

1. Calculate the k-component of the force onthe 2 m segment of the conductor that lies between x = 1.0m and x = 3.0 m.

Explanation / Answer

the force on the current in a bit of wire  dx   is given by .          dF = I Bydx              This force is in the -z direction (i.e. k component) and . total force in z direction = integralof ( I * 6.0 x2 dx)   from1.0 to 3.0   = .                =   5.5 * 6.0 * (1/3) x3   =   5.5 * 6.0 * (1/3) (3.03 -1.03) =    -286.0N       is the k component of forceon that segment

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