Question

A wire carrying a current i is kept in X-Y plane along the curve Y=A $sin\left(\frac{2\pi }{\lambda }x\right)$. A magnetic field B exists in the Z-direction as shown. Find the magnitude of the magnetic force on the portion of the wire between x=0 and $x=\lambda$

• A. $i\lambda B$
  
• B. Zero
• C. $\frac{i\lambda B}{2}$
  
• D. $\frac{3}{2i\lambda B}$

Answer 1

The correct option is A $i\lambda B$


The given portion of the curved wire may be treated as a straight wire AB of length $\lambda$ which experiences a magnetic force,
F=BI(length)
Here, length= $\lambda$
So, F=$i\lambda B$