Concept explainers
(a)
The relative permeability of the iron when the long iron-core solenoid is connected across
(a)
Answer to Problem 32SP
Solution:
Explanation of Solution
Given data:
The voltage across battery is
The current rises to
The current rises to
Formula used:
The expression of current through the coil in case of charging is written as,
Here,
The expression of time constant for the coil is written as,
Here,
The expression of inductance of the inductor is written as,
Here,
The relative permeability of the iron is expressed as,
Here,
Explanation:
Consider the expression of current through the coil when iron core is present.
Here,
Substitute
Simplify the expression.
Take
Solve for
Write the expression of time constant for the iron core solenoid.
Here,
Substitute
Consider the expression of current through the coil when iron core is removed.
Here,
Substitute
Simplify the expression.
Take
Solve for
Write the expression of time constant when the iron core is removed.
Here,
Substitute
Divide equation (1) and (2).
Simplify the expression.
Consider the expression of inductance of the inductor when iron core is present.
Here,
Consider the expression of inductance of the inductor when iron core is not present.
Here,
From equation (3) and (4)
Recall the expression of relative permeability of the iron.
Substitute
Substitute
Conclusion:
Therefore, the relative permeability of the iron is
(b)
The value of
(b)
Answer to Problem 32SP
Solution:
Explanation of Solution
Given data:
The voltage across battery is
From previous part, the value of time constant for air-cored solenoid is
The value of maximum current is
Formula used:
The Ohm’s Law states that the current through the resistor is directly proportional to the applied voltage across its terminal.
Mathematically,
Rearrange for
Here,
The expression of time constant for the coil is written as,
Here,
Explanation:
Recall the expression of Ohm’s law.
Solve for
Substitute
Consider the expression of time constant for the coil.
Solve for
Substitute
Conclusion:
Therefore, the inductance of the air-cored coil is
Want to see more full solutions like this?
Chapter 34 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
- It is desired to construct a solenoid that will have a resistance of 4.95 2 (at 20°C) and produce a magnetic field of 4.00 x 10-2 T at its center when it carries a current of 3.25 A. The solenoid is to be constructed from copper wire having a diameter of 0.500 mm. If the radius of the solenoid is to be 1.00 cm, determine the following. (The resistivity of copper at 20°C is 1.7 x 10-8 2. m.) (a) the number of turns of wire needed to build the solenoid turns. (b) the length the solenoid should have cmarrow_forwardBy how much is the approximation B = μonI [or in terms of 4πke Coulomb's constant ke, B = nI] in error at the center c² of a solenoid that is 10 cm long, has a diameter of 7 cm, is wrapped with n turns per meter, and carries a current I? Hint Compared to the exact expression, the approximation B = μonI is Select an answer by %.arrow_forwardIt is desired to construct a solenoid that will have a resistance of 5.75 (at 20°C) and produce a magnetic field of 4.00 × 10-2 T at its center when it carries a current of 4.85 A. The solenoid is to be constructed from copper wire having a diameter of 0.500 mm. If the radius of the solenoid is to be 1.00 cm, determine the following. (The resistivity of copper at 20°C is 1.7 x 10 Ω· m.) -8 (a) the number of turns of wire needed to build the solenoid Your response differs from the correct answer by more than 10%. Double check your calculations. turns (b) the length the solenoid should have cmarrow_forward
- It is desired to construct a solenoid that will have a resistance of 5.45 N (at 20°C) and produce a magnetic field of 4.00 × 10-2 T at its center when it carries a current of 4.35 A. The solenoid is to be constructed from copper wire having a diameter of 0.500 mm. If the radius of the solenoid is to be 1.00 cm, determine the following. (The resistivity of copper at 20°C is -8 1.7 x 10 Ω. m.) (a) the number of turns of wire needed to build the solenoid X turns (b).the.length the solenoid should have Enter a number. differs from the correct answer by more than 10%. Double check your calculations. cmarrow_forwardA shunt motor develops 80 Nm of torque when the flux density in the air gap is 1.0 Wb/m2 and the armature current is 15 A what is the torque when the flux density is 1.3 Wb/m2 and the armature current is 18 Aarrow_forwardIt is desired to construct a solenoid that will have a resistance of 4.65 N (at 20°C) and produce a magnetic field of 4.00 x 10-2T at its center when it carries a current of 3.85 A. The solenoid is to be constructed from copper wire having a diameter of 0.500 mm. If the radius of the solenoid is to be 1.00 cm, determine the following. (The resistivity of copper at 20°C is 1.7 x 10-8 n. m.) (a) the number of turns of wire needed to build the solenoid 853.2 v turns (b) the length the solenoid should have 426 Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. cmarrow_forward
- = 0.500 mm. The For a class demonstration, a professor needs to create a solenoid using copper wire with diameter d resistance of the solenoid needs to be 4.10 Q and the magnetic field of the solenoid with a current of 3.30 A should be 6.30 x 10-2 T. Assume the resistance does not change significantly with temperature, and the radius of the solenoid is 1.00 cm. (Use p = 1.70 x 10-8 0· m for the resistivity of copper.) (a) How many turns of wire does the professor need? turns (b) Determine the required length (in cm) of the solenoid. cmarrow_forwardACTIVITY #2 – PROBLEM-SOLVING A closely wound solenoid of 1,250 turns has an axial length of 98cm and a radius of 1.50 cm. When there is a current of 1.30 Amperes in the solenoid, what is the flux density on the axis at the center?arrow_forwardThe magnetic field in the core of an air-filled solenoid is 1.50 T, By how much will this magnetic field decrease if the ail is pumped out of the core while the current is held constant?arrow_forward
- A solenoid with 4 x 107turns/m has an iron core placed in it whose magnetic susceptibility is 4.0 x 103. (a) If a cent of 2.0 A flows through the solenoid, what is the magnetic field in the iron core? (b) What is the effective surface current formed by the aligned atomic current loops in the iron core? (c) What is the self-inductance of the filled solenoid?arrow_forwardA solenoid has a ferromagnetic core, n = 1000 turns per meter, and I = 5.0 A. If B inside the solenoid is 2.0 T, what is for the core material?arrow_forwardConsider a solenoid that is 15 cm long and 3 cm in diameter, with N = 500 turns. What value of current is required to give a field of magnitude B = 1.0 T? A Would this value be practical? Why or why not? (Assume the solenoid, made of 26 AWG copper wire melts at around 20 A.) The current is not high enough to melt the wire, making finding practical uses possible. The current is very high and would likely melt the wire, making this setup impractical.arrow_forward