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
IF THERE'S ANYTHING TO CALCULATE OR EXPLAIN PLEASE SHOW YOUR WORK
THANKS IN ADVANCE.
To find the answers to these questions, we can make use of the formulas for the magnetic field created by a current-carrying coil and how it changes with variations in current, number of turns per unit length, and relative permeability.
1) If a current 3I is sent through the coil:
The magnetic field strength B created at point M by a coil carrying current I is given by the formula B = µ₀ * N * I / (2π * r), where µ₀ is the permeability of free space, N is the number of turns, I is the current, and r is the distance from the coil to point M.
If the current is increased to 3I, the new magnetic field strength B' can be calculated by substituting the current value into the formula:
B' = µ₀ * N * (3I) / (2π * r)
= 3 * (µ₀ * N * I) / (2π * r)
= 3 * B
Therefore, the field strength at point M becomes 3 times the original strength, so the answer is a. 3B.
2) If the number of turns per unit length is doubled:
The original magnetic field strength B created at point M by a coil carrying current I is still given by the formula B = µ₀ * N * I / (2π * r), where N is the number of turns per unit length.
If the number of turns per unit length is doubled, the new magnetic field strength B' can be calculated by substituting 2N for N in the formula:
B' = µ₀ * (2N) * I / (2π * r)
= 2 * (µ₀ * N * I) / (2π * r)
= 2 * B
Therefore, the field strength at point M becomes twice the original strength, so the answer is a. 2B.
3) If the relative permeability of the core is changed to 10:
The original magnetic field strength B created at point M can be calculated using the formula B = µ₀ * N * I / (2π * r), where µ₀ is the permeability of free space.
If the relative permeability of the core changes to 10, we need to consider the new effective permeability, µ_eff, which is given by the product of µ₀ and the relative permeability of the core (µ = 10 in this case):
µ_eff = µ₀ * µ
= µ₀ * 10
= 10 * µ₀
The new magnetic field strength B' can be calculated using the formula:
B' = µ_eff * N * I / (2π * r)
= (10 * µ₀) * N * I / (2π * r)
= 10 * (µ₀ * N * I / (2π * r))
= 10 * B
Therefore, the field strength at point M becomes 10 times the original strength, so the answer is a. 10B.
In summary:
1) If the current is increased to 3I, the field strength becomes 3B.
2) If the number of turns per unit length is doubled, the field strength becomes 2B.
3) If the relative permeability of the core is changed to 10, the field strength becomes 10B.