Question

Infinite number of straight wires each carrying current I are equally placed as shown

in the figure. Adjacent wires have current in opposite direction. Net magnetic field at

point P is​

Answer 1

Explanation:

Zero

μ0I8πloge2r3–√

μ0I4πloge2r3–√

μ0I2πloge2r3–√

Answer :

D

Solution :

the magnetic field at O due to straight wire carrying current is

B→=μ04πIa[sin30∘+sin30∘]kˆ

=μ04πIa[12+12]kˆ=μ04πIakˆ

Total magnetic field at O due to current through all the straight parallel wires carrying currents

B→=B1kˆ+B2(−kˆ)+B3(kˆ)+B4(−kˆ)+...

B=B1−B2+B3−B4+...

=μ04πIa[1−12+13−14+...]

=μ04πIaloge(1+1)=μ04πIaloge2

Here, cos30∘=ar or a=rcos30∘=r3–√/2

∴B=μ04πI(r3–√/2)loge2=μ02πIr3–√loge2