Question

A wire of length 'L' carries current 'I' along the x-axis, A magnetic field B = B₀ `(hat "i" - hat "j" - hat "k")` T acts on the wire. The magnitude of the magnetic force acting on the wire is ____________.

Options

• `("I"  "L"  "B"_0)/2`

• `"I"  "L"  "B"_0`

• `sqrt2  "I"  "L"  "B"_0`

• 2 I L B₀

Answer 1

A wire of length 'L' carries current 'I' along the x-axis, A magnetic field B = B₀ `(hat "i" - hat "j" - hat "k")` T acts on the wire. The magnitude of the magnetic force acting on the wire is `sqrt2  "I"  "L"  "B"_0`.

Explanation:

The magnetic force acting on the wire is given by

`vec "F" = "I"  vecvarphi xx vec "B"` 

`= "I  L" hat "i" xx "B"_0 (hat "i" - hat j - hat "k")`

`= "I  L" hat "i" xx "B"_0 (hat "i" xx hat "i" - hat "i" xx hat "j" - hat "i" xx hat "k")`

`= "I L B"_0 [0 - hat "k" - (hat "j")]`

`= "I  L B"_0 [- hat"k" + hat "j"]`

`absvec"F" = "I L B"_0 sqrt((-1)^2 + (1)^2)`

`= sqrt2  "I L B"_0`