Problem 34.41 (RHK)
A wire of length 62.0 cm and mass 13.0 g is suspended by a pair of flexible leads in a magnetic field of 440 mT. We have to find the magnitude and the direction of the current in the wire required to remove the tension in the supporting leads.
Solution: Click For PDF Version
We fix a coordinate system as shown in the figure. Mass of the wire is 13.0 g.
The force due to gravitational pull of the Earth on the wire will be
Magnetic field acting on the wire is
Force on a wire of length, L, carrying current (A) in magnetic field, , is
Length of the wire is
The direction and magnitude of the current is so arranged that there is no tension in the supporting leads. That is
We note from the property of the cross-products that this condition determines the direction of the current. We have
And the magnitude of the current
The current flows from left-to-right, that is along the X-axis of the coordinate system shown in the figure.