Two long parallel straight conductors carry currents 7, and 12 `(I_(1)>I_(2))` When the currents are in the same direction, the magnetic field at a point midway between the wires is 20 mt. If the direction of Iz is reversed, the field becomes 50 mt. The ratio of the currents

Options

A. `(5)/(2)`
B. `(7)/(3)`
C. `(4)/(3)`
D. `(5)/(3)`

Answer

B

Explanation

When the current `I_(1) and I_(2)` are in the same direction , the magnetic field at point P is
`B_(1)=(mu_(0)I_(1))/(2pi(r"/"2))(mu_(0)I_(2))/(2pi(r"/"2))`
`2xx10^(-3)=(mu_(0))/(pir)(I_(1)-I_(2))`
When the direction of `I_(2)` is reversed , the magnetic field at same point P is
`B_(2)=(mu_(0))/(2pi)(I_(1))/((r"/"2))+(mu_(0))/(2pi)(I_(2))/((r"/"2))`
`50xx10^(-3)=(mu_(0))/(pir)(I_(1)-I_(2))`
Divide (i) by(ii) , we get
`(2)/(5)=(I_(1)-I_(2))/(I_(1)+I_(2)),2(I_(1)+I_(2))=5(I_(1)-I_(2))`
`(2)/(5)[(I_(1))/(I_(2))+1][(I_(1))/(I_(2))-1]:.(I_(1))/(I_(2))=(7)/(3)`