Question

Consider a straight conductor of length 2m carrying a current of 10 A in the +z direction. If the conductor is placed in a field of \(\vec B = 0.04\left( {{{\hat a}_y} - {{\hat a}_x}} \right)\) Wb/m², then the force per unit length on the conductor is
1. -0.04 (â_x + â_y) N / m
2. -0.4 (â_x + â_y) N / m
3. -0.08 (-â_x + â_y) N / m
4. -0.02 (â_x + â_y) N / m

Answer 1

Correct Answer - Option 2 : -0.4 (â_x + â_y) N / m

Concept:

The Lorentz force equation states that the force acting on a current carrying element is given by:

\(\vec F = I\left( {\vec L \times \vec B} \right)\)

I = current flowing through the conductor

L = length vector

B = magnetic field vector

Calculation:

\(\vec B = 0.04\left( {{{\hat a}_y} - {{\hat a}_x}} \right)wb/{m^2}\)

I = 10 A

From Lorentz force equation:

\(\vec F = I\left( {\vec L \times \vec B} \right)\)

= 10 (2â_z × 0.04 (â_y – â_x))

= 10 (0.08 (-â_x) – 0.08 â_y)

= -0.8 â_x – 0.8 â_y

= -0.8 (â­_x + â_y) N

Force per unit length is,

\(\frac{{\vec F}}{L} = \frac{{ - 0.8\left( {{{\hat a}_x} + {{\hat a}_y}} \right)}}{2}\)

= -0.4 (â_x + â_y)