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`?

Options

A. `2.1 N darr , 2.1 N darr , 1.68 N darr `
B. `1.68 darr , 2.1 N darr , 2.1 N darr `
C. `2.1 N darr , 1.68N darr, 2.1 N uarr `
D. `2.1 N uarr , 1.68 N darr , 2.1 N uarr `

Answer

C

Explanation

The magnetic field is in the direction east to west and in the cylindrical region of radius 10 cm.
a) A current carrying wire, intersects the axis. Force on wire,
`F = IBl = IB (2r) = 7 xx 1.5 xx 2 xx 1 xx 10^(-2)`
F=2.1 N Downwards.
b) By turinig the wire by an angle `45^@` in NE and NW direction the force remain the same, f = 2.1N Downwards
. c) Now the wire is lowered from the axis by a distance of 6.0 cm Length of wire inside cylindrical region is 16 cm now. So, the force is vertically downwards.
`F = IBl = 7 xx 1.5 xx 16 xx 10^(-2) = 1.68 N`