1)A coil of length 1cm has N turns and carries an electric current I. It creates at a point M a magnetic field of intensity B.
-If a current 3I is sent in the coil the field strength at M becomes:
a. 3B b. B/3 c. B
-If the number of turns per unit length is doubled the field strength at M becomes:
a. 2B b. B/2 c. B
2)If the coil of the preceding exercise the core of relative permeability is equal to 1 is replaced by another core of relative permeability=10 ,the field strength at M becomes:
a. 10B b. B/10 c. B
To determine the field strength at point M in both scenarios, we can use the formula for the magnetic field created by a current-carrying coil:
B = μ₀ * N * I * L / (2 * π * R)
where B is the magnetic field strength, μ₀ is the permeability of free space (constant value), N is the number of turns, I is the current, L is the length of the coil, and R is the distance from the coil to point M.
1) If a current 3I is sent through the coil:
Considering that the length of the coil and the distance to point M remain constant, the only changing parameters are the number of turns (N) and the current (I).
According to the formula, the field strength (B) is directly proportional to the number of turns (N). Therefore, when the current is tripled (3I), the field strength at point M becomes 3B.
Thus, the answer is a. 3B.
2) If the number of turns per unit length is doubled:
In this case, the length of the coil (L) is not provided, so we can assume L = 1 cm.
The formula for the field strength (B) indicates that it is directly proportional to the number of turns (N). Therefore, when the number of turns per unit length is doubled, the total number of turns (N) will be twice the initial value.
Since all the other parameters remain constant, the field strength at point M will also be doubled.
Thus, the answer is a. 2B.
3) If the coil's core has a relative permeability of 10:
In this case, we don't have the specific value for the relative permeability of free space (μ₀), but we can assume it to be 1 for simplicity.
The formula for the field strength (B) indicates that it is directly proportional to the relative permeability (μ₀) as well as the number of turns (N).
When the relative permeability of the core is increased to 10, the field strength will also increase by a factor of 10.
Thus, the answer is a. 10B.