MP Board · Class 10 · Science · Magnetic Effects of Electric CurrentA uniform magnetic field of magnitude $1.5 \times 10^{-2}\text{ T}$ points vertically downward. A straight wire of length $0.8\text{ m}$ carries a current of $5.0\text{ A}$ in a horizontal direction from east to west. Calculate the magnitude and direction of the magnetic force acting on the wire.

To calculate the magnetic force acting on the current-carrying wire, we use the formula: $$F = I \cdot l \cdot B \cdot \sin(\theta)$$

Given Data:

• Magnetic field ($B$) = $1.5 \times 10^{-2}\text{ T}$ (vertically downward)
• Length of the wire ($l$) = $0.8\text{ m}$
• Current ($I$) = $5.0\text{ A}$ (horizontal, east to west)
• Angle between the current direction and magnetic field ($\theta$) = $90^\circ$ (since the wire is horizontal and the magnetic field is vertical)

Step-by-Step Calculation:

1. Substitute the given values into the formula: $$F = (5.0\text{ A}) \times (0.8\text{ m}) \times (1.5 \times 10^{-2}\text{ T}) \times \sin(90^\circ)$$
2. Since $\sin(90^\circ) = 1$, the equation simplifies to: $$F = 5.0 \times 0.8 \times 1.5 \times 10^{-2}$$
3. Calculate the product of the numbers: $$5.0 \times 0.8 = 4.0$$ $$4.0 \times 1.5 = 6.0$$
4. Therefore, the magnitude of the force is: $$F = 6.0 \times 10^{-2}\text{ N} = 0.06\text{ N}$$

Direction of the Force:\nUsing Fleming's Left-Hand Rule:

• Point your forefinger in the direction of the magnetic field (vertically downward).
• Point your middle finger in the direction of the current (east to west).
• The extended thumb will point towards the South direction.

Answer:\nThe magnitude of the magnetic force is $0.06\text{ N}$ and its direction is towards the South.