A uniform magnetic field of `1*5T` is in cylindrical region of radius `10*0cm` with its direction parallel to the axis along east to west. A wire carrying current of `7*0A` in the north to south direction passes through this region. What is the magnitude and direction of the force on the wire if (a) the wire intersects the axes, (b) the wire is turned from N-S to north east-south west direction, (c) the wire in the N-S direction is lowered from the axis by a distance `6*0cm`?

Explanation

Here, `B=1*5T`, `I=7*0A`
(a) Length of the wire in a cylindrical magnetic field, is equal to the diameter of the cylinderical region i.e.
`l=20cm=0*20m`. Angle between current and magnetic field `theta=90^@`
`:.` Force on the wire, `F=BIl sin theta=1*5xx7*0xx0*20xxsin90^@=2*1N`
The direction of this force is vertically downwards, using Fleming's left hand rule.
(b) When the wire is turned from N-S to northeast-northwest direction, the length of the wire in the cylindrical region of magnetic field is `l_1` and `theta=45^@`
`:.` Force on the wire, `F_1=BIl_1sin45^@=BIl [ :' l_1sin45^@=l]`
or `F_1=1*5xx7*0xx0*20=2*1N`
The direction of this force is vertically downwards, using Fleming's Left hand Rule.
(c) When the wire is lowered by `6*0cm` i.e. at position CD in figure., then length of wire in magnetic fied, `l_2=2x`
where, `x xx x=4xx(10+6)` or `x=8cm`.
`:. l_2=2xx8cm=16cm=0*16m`.
Force on wire, `F_2=BIl_2=1*5xx7xx0*16=1*68N` vertically downwards.