A winding wire which is used to prepare a solenoid of length 80 cm can bear a maximum cuurent of 10 A. the cross-sectional radius of the solenoid is 3 cm. what should be the length of the winding wire if a magnetiic field of 0.2 T is to be produced at the centre of the solenoid along its axis?

Options

A. `1.2 xx 10^(2)` m
B. `4.8 xx 10^(2)` m
C. `2.4 xx 10^(3)` m
D. `6 xx 10^(3)` m

Answer

C

Explanation

`B = mu_(0) ni implies mu_(0) ""(N)/(I) i=0.2`
`implies N = (4 xx 10^(4))/(pi)`
Length of wire (L) = `2pi r xx N = 2pi xx 3 xx 10^(-2) xx (4 xx 10^(-4))/(pi)`
`=2.4 xx 10^(-3)` m