Amperes Law
Q. According to Ampere's Law, the line integral of the magnetic field B around a closed path is equal to what?
A.
Zero
B.
The product of permeability and current
C.
The product of permittivity and charge
D.
The electric field times the area
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Solution
Ampere's Law states that the line integral of the magnetic field B around a closed path is equal to μ₀ times the total current I enclosed by the path.
Correct Answer: B — The product of permeability and current
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Q. According to Ampere's Law, the line integral of the magnetic field B around a closed loop is equal to what?
A.
0
B.
μ₀ times the total current through the loop
C.
μ₀ times the total charge
D.
None of the above
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Solution
Ampere's Law states ∮B·dl = μ₀I_enc, where I_enc is the enclosed current.
Correct Answer: B — μ₀ times the total current through the loop
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Q. According to Ampere's Law, what is the line integral of the magnetic field around a closed loop equal to?
A.
0
B.
μ₀ times the total current through the loop
C.
μ₀ times the total charge
D.
None of the above
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Solution
Ampere's Law states that the line integral of B around a closed loop is μ₀ times the total current through the loop.
Correct Answer: B — μ₀ times the total current through the loop
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Q. According to Ampere's Law, what is the magnetic field inside a long straight conductor carrying current I?
A.
Zero
B.
μ₀I/2πr
C.
μ₀I/4πr
D.
μ₀I/πr
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Solution
Inside a long straight conductor, the magnetic field is zero because the contributions from all parts of the conductor cancel out.
Correct Answer: A — Zero
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Q. For a closed loop of wire carrying current, what does the line integral of the magnetic field equal?
A.
Zero
B.
The product of current and resistance
C.
μ₀ times the total current enclosed
D.
The electric field times the area
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Solution
According to Ampere's Law, the line integral of the magnetic field around a closed loop equals μ₀ times the total current enclosed by the loop.
Correct Answer: C — μ₀ times the total current enclosed
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Q. For a cylindrical conductor of radius R carrying current I, what is the magnetic field at a point outside the conductor?
A.
0
B.
μ₀I/2πR
C.
μ₀I/4πR
D.
μ₀I/πR
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Solution
Using Ampere's Law, B = μ₀I/2πR for points outside the cylindrical conductor.
Correct Answer: B — μ₀I/2πR
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Q. For a cylindrical conductor of radius R carrying current I, what is the magnetic field at a point outside the cylinder?
A.
0
B.
μ₀I/2πr
C.
μ₀I/4πr
D.
μ₀I/πr
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Solution
For points outside the cylinder, B = μ₀I/2πr.
Correct Answer: B — μ₀I/2πr
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Q. For a solenoid of length L and n turns per unit length carrying current I, what is the magnetic field inside the solenoid?
A.
μ₀nI
B.
μ₀I/n
C.
μ₀I/L
D.
μ₀nI/L
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Solution
The magnetic field inside a solenoid is given by B = μ₀nI.
Correct Answer: A — μ₀nI
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Q. For a solenoid of length L, radius R, and carrying current I, what is the magnetic field inside the solenoid?
A.
μ₀nI
B.
μ₀I/L
C.
μ₀I/2L
D.
μ₀I/4L
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Solution
Using Ampere's Law, B = μ₀nI where n is the number of turns per unit length.
Correct Answer: A — μ₀nI
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Q. For a toroidal solenoid with N turns and radius R carrying current I, what is the magnetic field inside the toroid?
A.
μ₀NI/2πR
B.
μ₀NI/R
C.
μ₀NI/4πR
D.
μ₀NI/2R
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Solution
The magnetic field inside a toroid is given by B = μ₀NI/2πR.
Correct Answer: B — μ₀NI/R
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Q. If a circular loop of radius R carries a current I, what is the magnetic field at the center of the loop according to Ampere's Law?
A.
μ₀I/2R
B.
μ₀I/4R
C.
μ₀I/R
D.
μ₀I/πR
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Solution
The magnetic field at the center of a circular loop is given by B = (μ₀I)/(2R).
Correct Answer: A — μ₀I/2R
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Q. If a circular loop of radius R carries a current I, what is the magnetic field at the center of the loop?
A.
μ₀I/2R
B.
μ₀I/4R
C.
μ₀I/R
D.
μ₀I/8R
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Solution
Using Ampere's Law, B = μ₀I/2R at the center of a circular loop.
Correct Answer: A — μ₀I/2R
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Q. If a long straight conductor carries a current I, what is the magnetic field at a distance r from the wire?
A.
μ₀I/(2πr)
B.
μ₀I/(4πr²)
C.
μ₀I/(2r)
D.
μ₀I/(πr²)
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Solution
According to Ampere's Law, the magnetic field B at a distance r from a long straight conductor carrying current I is given by B = μ₀I/(2πr).
Correct Answer: A — μ₀I/(2πr)
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Q. If a long straight conductor carries a current I, what is the magnetic field B at a distance r from the wire?
A.
B = μ₀I/(2πr)
B.
B = μ₀I/(4πr²)
C.
B = μ₀I/(2r)
D.
B = μ₀I/(πr²)
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Solution
According to Ampere's Law, the magnetic field B around a long straight conductor is given by B = μ₀I/(2πr).
Correct Answer: A — B = μ₀I/(2πr)
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Q. If a long straight wire carries a current I, what is the magnetic field at a distance r from the wire according to Ampere's Law?
A.
μ₀I/(2πr)
B.
μ₀I/(4πr²)
C.
I/(2πr)
D.
μ₀I/(r)
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Solution
Using Ampere's Law, the magnetic field B at a distance r from a long straight wire carrying current I is given by B = μ₀I/(2πr).
Correct Answer: A — μ₀I/(2πr)
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Q. If a solenoid has n turns per unit length and carries a current I, what is the magnetic field inside the solenoid?
A.
0
B.
μ₀nI
C.
μ₀I/n
D.
μ₀I
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Solution
The magnetic field inside a solenoid is given by B = μ₀nI.
Correct Answer: B — μ₀nI
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Q. If a wire carries a current of 5 A and is placed in a magnetic field of 0.1 T, what is the force per unit length on the wire?
A.
0.5 N/m
B.
1 N/m
C.
0.2 N/m
D.
0.1 N/m
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Solution
Using the formula F = BIL, where B is the magnetic field, I is the current, and L is the length of the wire (1 m), F = 0.1 T * 5 A * 1 m = 0.5 N.
Correct Answer: B — 1 N/m
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Q. If a wire carries a current of 5 A, what is the magnetic field at a distance of 0.1 m from the wire?
A.
0.1 T
B.
0.2 T
C.
0.5 T
D.
1.0 T
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Solution
Using Ampere's Law, B = μ₀I/2πr, where μ₀ = 4π × 10^-7 Tm/A, we find B = (4π × 10^-7)(5)/(2π(0.1)) = 0.1 T.
Correct Answer: B — 0.2 T
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Q. If the current in a circular loop is doubled, how does the magnetic field at the center change?
A.
Remains the same
B.
Doubles
C.
Halves
D.
Quadruples
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Solution
The magnetic field at the center of a loop is directly proportional to the current.
Correct Answer: B — Doubles
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Q. If the current in a circular loop is doubled, how does the magnetic field at the center of the loop change?
A.
It remains the same
B.
It doubles
C.
It quadruples
D.
It halves
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Solution
The magnetic field at the center of a circular loop is directly proportional to the current; thus, if the current is doubled, the magnetic field also doubles.
Correct Answer: B — It doubles
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Q. If the current in a wire is doubled, how does the magnetic field at a point 1 meter away change?
A.
It doubles
B.
It quadruples
C.
It remains the same
D.
It halves
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Solution
The magnetic field is directly proportional to the current, so it doubles.
Correct Answer: A — It doubles
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Q. If the current in a wire is doubled, how does the magnetic field at a point near the wire change according to Ampere's Law?
A.
It remains the same
B.
It doubles
C.
It quadruples
D.
It halves
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Solution
According to Ampere's Law, the magnetic field is directly proportional to the current, so doubling the current will double the magnetic field.
Correct Answer: B — It doubles
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Q. If the current in a wire is reversed, what happens to the direction of the magnetic field around the wire?
A.
It remains the same
B.
It reverses direction
C.
It becomes zero
D.
It doubles in strength
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Solution
Reversing the current in a wire reverses the direction of the magnetic field around it.
Correct Answer: B — It reverses direction
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Q. If the magnetic field around a closed loop is constant, what can be said about the current through the loop?
A.
It is zero
B.
It is variable
C.
It is constant
D.
It is infinite
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Solution
If the magnetic field around a closed loop is constant, the current through the loop must also be constant according to Ampere's Law.
Correct Answer: C — It is constant
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Q. If the radius of a circular loop carrying current is doubled, how does the magnetic field at the center change?
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
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Solution
The magnetic field at the center of a circular loop is inversely proportional to the radius; thus, doubling the radius halves the magnetic field.
Correct Answer: B — It halves
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Q. If the radius of a circular loop carrying current is doubled, what happens to the magnetic field at the center of the loop?
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
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Solution
The magnetic field at the center of a circular loop is given by B = (μ₀I)/(2r). If the radius is doubled, the magnetic field strength is halved.
Correct Answer: B — It halves
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Q. If the radius of a circular loop carrying current is halved, how does the magnetic field at the center change?
A.
Remains the same
B.
Doubles
C.
Halves
D.
Quadruples
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Solution
The magnetic field at the center is inversely proportional to the radius, so it quadruples.
Correct Answer: D — Quadruples
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Q. If two parallel wires carry currents in the same direction, what is the interaction between the magnetic fields they produce?
A.
They repel each other
B.
They attract each other
C.
No interaction
D.
They cancel each other out
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Solution
Two parallel wires carrying currents in the same direction will attract each other due to the magnetic fields they produce.
Correct Answer: B — They attract each other
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Q. In a circular path of radius r around a long straight wire carrying current I, what is the line integral of the magnetic field?
A.
0
B.
μ₀I
C.
μ₀I/2
D.
μ₀I/4
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Solution
The line integral of B around the path is equal to μ₀I by Ampere's Law.
Correct Answer: B — μ₀I
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Q. In a closed loop, if the net current is zero, what can be said about the magnetic field according to Ampere's Law?
A.
The magnetic field is zero everywhere
B.
The magnetic field is uniform
C.
The magnetic field can be non-zero
D.
The magnetic field is only zero at the center
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Solution
According to Ampere's Law, if the net current through a closed loop is zero, the line integral of the magnetic field around that loop is also zero, but the magnetic field can still be non-zero in some regions.
Correct Answer: C — The magnetic field can be non-zero
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