A rectangular coil consists of N = 120 closely wrapped turns and has dimensions
ID: 1495076 • Letter: A
Question
A rectangular coil consists of N = 120 closely wrapped turns and has dimensions a = 0.400 m and b = 0.300 m. The coil is hinged along the y axis, and its plane makes an angle = 30.0° with the x axis (figure). (a) What is the magnitude of the torque exerted on the coil by a uniform magnetic field B = 0.690 T directed in the positive x direction when the current is I = 1.20 A in the direction shown? N · m (b) If you are looking downward from the positive y direction, what is the expected direction of rotation of the coil? clockwise counterclockwise
Explanation / Answer
The torque on a current loop is given by ... v_ = ( v_ ) × ( v_B ) where
... (v_ ) = torque vector ... ( v_ ) = magnetic dipole moment vector of the
current loop ... ( v_B ) = magnetic field vector ... that is, in terms of the magnitude
of vectors ... = B sin ... where ... = angle between the vectors ( v_ ) and
( v_B ) ... using the right hand rule, with the fingers of the right hand curled along
the direction of current flow and the thumb extending outward perpendicular to
the plane of the current loop, we find that ... = 90° - 30° = 60° ... since the
magnetic field vector ( v_B ) is along the positive x-axis ... moreover ...
... = N i L W ... N = 102 = number of windings (turns) of the current loop ...
... L and W are the length and width of the rectangular loop ... that is ...
... = B sin = N i L W B sin 60° ... substituting the values, we get ...
... = ( 102 ) ( 1.20 A ) ( 0.400 m ) ( 0.300 m ) ( 0.872 T ) sin 60°
...... = 11.1 A • m ² • T ... and since ... A --> C / s ... F = QvB --> N = C • ( m / s ) • T
or ... T --> N • s / ( C • m ) ... we find that ...
... A • m ² • T = ( C / s ) • m ² • [ N • s / ( C • m ) ] = N • m ... that is ...
... = 11.1 N • m
b. Clockwise direction