A single circular loop of wire radius `0.02 m` carries a current of `8.0 A`. It is placed at the centre of a solenoid that the length `0.65 m`, radius `0.080 m` and 1300 turns.

Options

A. The value of the current in the solenoid so that the magnetic field at the centre of the loop becomes zero,is equal to `4.4 A`.
B. The value of the current in the solenoid so that the magnetic field at the centre of the loop becomes zero,is equal to `10 A`.
C. The magnitude of the total magnetic field at the centre of the loop (due to both the loop and the solenoid)if the current in the loop is reversed in direction from that needed to make the total field equal to zero Tesla, is `8pixx10^(-3)T`.
D. The magnitude of the total magnetic field at the centre of the loop (due to both the loop and the solenoid)if the current in the loop is reversed in direction from that needed to make the total field equal to zero Tesla, is `16pixx10^(-3)T`.

Answer

B,D

Explanation

For given condition
Magnitude of `B_(solienoid)`=Magnitude of `B_("loop")`
`mu_(0)ni=(mu_(0)I)/(2R)` here`n="Total no. of turn"/"Total length"=1300/0.65`
`i=1/(2R)xx1/n=(8xx0.65)/(2xx0.02xx1300xx10^(-2))=10 A`
For given condition:
Total magnetic field at the centre of loop
`=|B_("loop")|+|B_("solenoid")| :' |B_("loop")|=|B_("solenoid")|`
`=2|B_("loop") =2xx(mu_(o)I)/(2R)`
`=(2xx4pixx10^(-7)xx8)/(2xx0.02xx10^(-2))=16pixx10^(-3) T`.