A long straight conductor carrying current `I_1` is placed in the plane of a ribbon carrying current `I_2` parallel to the previous one. The width of the ribbon is b and the straight conductor is at a distance a from the near endge. Find the force of attraction between the two.

Options

A. `(mu_(0)I_(1)I_(2))/(2pib)log((a+b)/(a))`
B. `(mu_(0)I_(1)I_(2))/(2pib)log((a)/(a+b))`
C. `(mu_(0)I_(1)I_(2))/(2pib)log((a)/(b))`
D. `(mu_(0)I_(1)I_(2))/(2pib)log(((a+b))/(a))`

Answer

A

Explanation

Consider an elementary strip of width `dx`on the sheet at a distance `x` from the wire.
Force on this element is : `dF=(mu_(0)I_(1))/(2pix)I_(2)dx`
Total force on unit length of sheet is
`F=int_(a)^(a+b)(mu_(0)I_(1))/(2pix)I_(2)dx`
`F=(mu_(0)I_(1)I_(2))/(2pi)int_(a)^(a+b)(1)/(x)dx=(mu_(0)I_(1)I_(2))/(2pia)log((a+b)/(b))`