a) a wire 75 cm long lying along the x-axis carries a current of 2A in the posit

Question

a) a wire 75 cm long lying along the x-axis carries a current of 2A in the positive x-direction. A magnetic field measured in T is given by B = 0.03 i + 0.02 j + 0.04 k. Find all the components of the magnetic force on wire. b) The figure on the right shows 100 turns of a thin rectangular loop of dimensions 8 cm by 15 cm. It carries a current of 0.5 A in the direction shown. If the plane of the coil is 30 degree from the yz plane and B = 0.4 k, find I) the magnitude and direction of the torque acting on the coil. II) the work needed to turn the coil clockwise (as seen from the top of the y-axis)from its present position to one where the plane of the coil is along the yz plane(Parallel to B field).

Explanation / Answer

L = 75 cm , I = 2 i ,

B = 0.03i +0.02 j +0.04 k

F = L(IxB)

F = 0.75(2i x(0.03i +0.02 j +0.04 k))

F = 0.75*2*0.02 k - 0.75*2*0.04 j

F = 0.03 k - 0.06 j

F = 0*i - 0.06 j +0.03 k

b) A = 8cm*15cm , N = 100, I = 0.5 A

B = 0.4 k, theta = 30 degrees

(I) TOrque = MXB = MB sin(theta)

M = NAI

T = NBAI sin(theta)

T = 100*0.4*0.08*0.15*0.5*sin(30)

T = 0.12 i N.m

direction is along x direction

(II) Work done equal to change in potential energy

W = U2 - U1

W = MBcos(0) - MBcos(30)

W =100*0.4*0.08*0.15*0.5*(cos0 - cos(30))

W = 0.032 J

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