Consider a thin, infinitely long conducting ribbon that carries a uniform current density j (current per unit area). The width of the ribbon is w and its thickness s is extremely small (s≪w). P is a point in the plane of the ribbon, at a large distance (x≫s) from the ribbon edge. (See the figure below)
What is the magnitude of the magnetic field B (in T) at point P for the following values of w , j, s and x?
w= 5 cm; s= 0.1 cm; j=1A/m2 and x= 23 cm.
Honor code!
oh! boys where is the honour in this!
To find the magnitude of the magnetic field at point P, we can use the Biot-Savart Law. According to the law, the magnetic field produced by a current element in a wire is directly proportional to the current, its length, and varies inversely with the square of the distance from the wire.
The formula for calculating the magnetic field at point P is given by:
B = μ₀ * j * l / (2π * r)
Where:
- B is the magnetic field
- μ₀ is the permeability of free space (4π * 10⁻⁷ T*m/A)
- j is the current density
- l is the length of the wire element generating the magnetic field
- r is the distance from the wire element to the point P
In this specific case, we have a thin ribbon with an infinitely long length, so the length of the wire element doesn't affect the calculation. We only need to consider the current density, the distance from the ribbon edge, and the distance to point P.
Given:
w = 5 cm (convert it to meters: 0.05 m)
s = 0.1 cm (convert it to meters: 0.001 m)
j = 1 A/m²
x = 23 cm (convert it to meters: 0.23 m)
To calculate the length of the current element, we need to account for the thickness of the ribbon (s). Since s is much smaller than the width of the ribbon (w), we can assume that the current flows uniformly through a rectangular cross-section.
The length of the current element (l) is given by:
l = w
Now, we can calculate the distance from the wire element to point P (r). Since P is at a large distance (x ≫ s) from the ribbon edge, we can approximate the distance to be x.
Plugging in the values into the formula:
B = (4π * 10⁻⁷ T*m/A) * (1 A/m²) * (0.05 m) / (2π * 0.23 m)
Simplifying further,
B = (2 * 10⁻⁷ T * m² / A) * (0.05 m) / (0.23 m)
B = 4.35 * 10⁻⁷ T
Therefore, the magnitude of the magnetic field at point P is approximately 4.35 * 10⁻⁷ Tesla (T).