Question

A straight conductor carries a current of 5 A. An electron travelling with a speed of $ 5\times {{10}^{6}}m{{s}^{-1}} $ parallel to the wire at a distance of 0.1 m from the conductor, experiences a force of:

• A. $ 8\times {{10}^{-20}}N $
• B. $ 3.2\times {{10}^{-19}}N $
• C. $ 8\times {{10}^{-18}}N $
• D. $ 1.6\times {{10}^{-19}}N $
• E. zero

Answer 1

Answer: (C)

$ F=Bev $ and $ B=\frac{{{\mu }_{0}}i}{2\pi r} $
$ \therefore $ $ F=\frac{{{\mu }_{0}}i}{2\pi r}\times ev $
$ =\frac{4\pi \times {{10}^{-7}}\times 5}{2\pi \times 0.1}\times 1.6\times {{10}^{-19}}\times 5\times {{10}^{6}} $
$ =8\times {{10}^{-18}}N $