Question

A 4.0 cm long straight wire carrying a current of 8A is placed perpendicular to an uniform magnetic field of strength 0.15 T. The magnetic force on the wire is ______ mN.

Hint:

Use the formula for the magnetic force on a current-carrying wire in a magnetic field. Remember to convert the length to meters.

Answer 1

Correct Answer: 48

This problem requires the calculation of the magnetic force on a straight current-carrying wire positioned perpendicularly to a uniform magnetic field.

Concept Used:

The magnetic force (\( F_m \)) acting on a straight wire segment of length \( L \) carrying a current \( I \) within a uniform magnetic field of strength \( B \) is quantified by the equation:

\[ F_m = I L B \sin\theta \]

Here, \( \theta \) represents the angle between the direction of current flow along the wire and the direction of the magnetic field.

Step-by-Step Solution:

Step 1: Enumerate the provided parameters and ensure they are in SI units.

The given values are:

• Wire length, \( L = 4.0 \, \text{cm} = 4.0 \times 10^{-2} \, \text{m} \)
• Current, \( I = 8 \, \text{A} \)
• Magnetic field strength, \( B = 0.15 \, \text{T} \)

Since the wire is oriented perpendicular to the magnetic field, the angle \( \theta \) is \( 90^\circ \).

Step 2: Insert the established values into the magnetic force formula.

The formula for the magnitude of the magnetic force is:

\[ F_m = I L B \sin\theta \]

With the given values substituted:

\[ F_m = (8 \, \text{A}) \times (4.0 \times 10^{-2} \, \text{m}) \times (0.15 \, \text{T}) \times \sin(90^\circ) \]

Step 3: Determine the magnetic force in Newtons.

As \( \sin(90^\circ) = 1 \), the calculation simplifies to:

\[ F_m = 8 \times 4.0 \times 10^{-2} \times 0.15 \] \[ F_m = 8 \times 0.04 \times 0.15 \] \[ F_m = 0.32 \times 0.15 \] \[ F_m = 0.048 \, \text{N} \]

Final Computation & Result:

The problem requires the magnetic force expressed in milliNewtons (mN). The conversion from Newtons (N) to milliNewtons (mN) uses the factor \( 1 \, \text{N} = 1000 \, \text{mN} \).

\[ F_m = 0.048 \, \text{N} \times \frac{1000 \, \text{mN}}{1 \, \text{N}} = 48 \, \text{mN} \]

The calculated magnetic force on the wire is 48 mN.