A wire which is 10 m long carries a current of 5 A, which is placed at an angle of 90 degrees to a uniform magnetic field. If a force of 8 N acts on it, find the value of B ?

Options

A. 0.16 T
B. 27T
C. 18.7 T
D. 6.70T

Explanation

To solve the problem, we will use the formula for the magnetic force acting on a current-carrying wire in a magnetic field. The formula is given by:

\[ F = I \cdot B \cdot L \cdot \sin(\theta) \]

Where:
- \( F \) is the force acting on the wire (in Newtons),
- \( I \) is the current flowing through the wire (in Amperes),
- \( B \) is the magnetic field strength (in Tesla),
- \( L \) is the length of the wire (in meters),
- \( \theta \) is the angle between the wire and the magnetic field.

Given:
- \( F = 8 \, \text{N} \)
- \( I = 5 \, \text{A} \)
- \( L = 10 \, \text{m} \)
- \( \theta = 90^\circ \)

Since the wire is at an angle of \( 90^\circ \) to the magnetic field, we know that \( \sin(90^\circ) = 1 \).

Now, we can rearrange the formula to solve for \( B \):

\[ B = \frac{F}{I \cdot L \cdot \sin(\theta)} \]

Substituting the known values into the equation:

1. Substitute \( F = 8 \, \text{N} \), \( I = 5 \, \text{A} \), \( L = 10 \, \text{m} \), and \( \sin(90^\circ) = 1 \):

\[ B = \frac{8}{5 \cdot 10 \cdot 1} \]

2. Calculate the denominator:

\[ 5 \cdot 10 = 50 \]

3. Now substitute back into the equation:

\[ B = \frac{8}{50} \]

4. Simplify the fraction:

\[ B = 0.16 \, \text{T} \]

Thus, the value of the magnetic field \( B \) is \( 0.16 \, \text{Tesla} \).