Question

A horizontal rod of mass 20 g and length 40 cm is placed on a smooth plane inclined at an angle of 60° with the horizontal, with the length of the rod parallel to the edge of the inclined plane. A uniform magnetic field of induction B is applied vertically downwards. If the current through the rod is 1.73 ampere, then the value of B for which the rod remains stationary on the inclined plane is ____________.

Options

• 0.5 T

• (1.73)^-1 T

• 1 T

• `sqrt2  (1.73) "T"`

Answer 1

A horizontal rod of mass 20 g and length 40 cm is placed on a smooth plane inclined at an angle of 60° with the horizontal, with the length of the rod parallel to the edge of the inclined plane. A uniform magnetic field of induction B is applied vertically downwards. If the current through the rod is 1.73 ampere, then the value of B for which the rod remains stationary on the inclined plane is 0.5 T.

Expanation:

Let F_m be the force arising due to magnetic field, then the given situation can be drawn as follows

`"f"_"m" = "BI"l Rightarrow "mg sin"  60° = "BI"l "cos"  60°`

`Rightarrow "B" = (0.02 xx 10 xx sqrt3)/(0.4 xx 1.73)` = 0.5 "T"