A rectangular loop has dimensions 0.530 m by 0.275 m. The loop is hinged along t

Question

A rectangular loop has dimensions 0.530 m by 0.275 m. The loop is hinged along the x-axis and lies in the xy-plane (see the figure below). A uniform magnetic field of 1.65 T is directed at an angle of 40.0 degree with respect to the positive y-axis and lies parallel everywhere to the yz-plane. The loop carries a current of 0.865 A in the direction shown. (Ignore gravitation.) In what direction is magnetic force exerted on wire segmental ab? What is the direction of the magnetic torque associated with this force, as computed with respect to the x-axis? What is the direction of the magnetic force exerted on segmented cd? What is the direction of the magnetic torque associated with this force, again computed with respect to the x-axis? Can the forces examined in parts (a) and (b) combine to cause the loop to rotate around the x-axis? Can they affect the motion of the loop in anyway? Explain. What is the direction (in the yz-plane) of the magnetic force exerted on segment bc? counterclockwise from the +y-axis Measuring torques with respect to the x-axis, what is the direction of the torque exerted by the force on segment bc? Looking toward the origin along the positive x-axis, will the loop rotate clockwise or counterclockwise? Compute the magnitude of the magnetic moment of the loop. What is the angle between the magnetic moment vector and the magnetic field? counterclockwise from the magnetic moment vector Compute the torque on the loop using the values found for the magnetic moment and magnetic field.

Explanation / Answer

part a )

current in ab segment is in the +y direction . by right hand rule magnetic force in +x direction

this force rotate segment ab in a clock wise direction about z axis

torque is in the -z direction

part b )

current in cd segment is in the -y direction , by right hand rule

magnetic force -x direction

this force rotate segment ab in a counterclock wise direction about z axis

torque direction is in +z direction

part c )

No , because Both the forces and the torques are equal in magnitude and opposite in direction, so they sum to zero and cannot affect the motion of the loop.

part d )

The magnetic force is perpendicular to both the direction of the current in bc and the magnetic field .

in the yz plane at 130 degree counterclock wise from +y axis

The force acting on segment bc tends to rotate it counterclockwise about the x axis, so the torque is in +x direction

part e )

loops tends to rotate counterclockwise about x axis

part f )

mu = IAN

mu = 0.865 * [ .530 * .275] = 0.126 A-m^2

part g )

90 + 40 = 130 degree

part h )

t = mu x B = mu*B*sintheta

t = 0.126 * 1.65 * sin130

t = 0.159 N-m

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