Question

A wire, carrying a current i, is kept in the x−y plane along the curve y=A sin(2πλx). A magnetic field B exists in the z direction. Find the magnitude of the magnetic force on the portion of the wire between x = 0 and x = λ.

Answer 1

Answer:

12

Explanation:

Answer 2

The magnetic force’s magnitude on the wire’s portion between x = λ and x = 0 is iλB.

Explanation:

Given:

Flowing electric current via the wire = i

In the x−y plane, along the curve, the wire is kept, $y=A \sin 2 \pi \lambda x$

In the z direction, magnetic field (B) exists.

We must see that on the wire portion, the magnetic force between x = λ and x = 0.

Magnetic force is shown as

$F \rightarrow=i l \rightarrow \times B \rightarrow$

For a small element dl,

$d F \rightarrow=i d l \times B \rightarrow$

On the full wire, the effective force is equal to the starlight wire’s force of length λ positioned along the x axis.

So,

$F=i B \int 0 \lambda d l$

$\Rightarrow F=i \lambda B$