Magnetism & EMI
Q. What is the magnetic field at a point due to a long straight current-carrying conductor using Biot-Savart Law?
A.
μ₀I/(2πr)
B.
μ₀I/(4πr²)
C.
μ₀I/(2r)
D.
μ₀I/(4r)
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Solution
The magnetic field B at a distance r from a long straight conductor carrying current I is given by B = μ₀I/(2πr) according to Biot-Savart Law.
Correct Answer: A — μ₀I/(2πr)
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Q. What is the magnetic field at a point on the axis of a circular loop of radius R carrying current I?
A.
μ₀I/(2R)
B.
μ₀I/(4R)
C.
μ₀I/(2R²)
D.
μ₀I/(2√2R)
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Solution
The magnetic field on the axis of a circular loop is given by B = (μ₀I/(2R)) * (1/(1 + (z/R)²)^(3/2)) where z is the distance along the axis.
Correct Answer: D — μ₀I/(2√2R)
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Q. What is the magnetic field at a point on the axis of a circular loop of radius R carrying a current I at a distance x from the center?
A.
(μ₀I)/(2R) * (R²/(R²+x²)^(3/2))
B.
(μ₀I)/(4R) * (R²/(R²+x²)^(3/2))
C.
(μ₀I)/(2R) * (1/(R²+x²)^(3/2))
D.
(μ₀I)/(4R) * (1/(R²+x²)^(3/2))
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Solution
The magnetic field on the axis of a circular loop is given by B = (μ₀I)/(2R) * (R²/(R²+x²)^(3/2)).
Correct Answer: A — (μ₀I)/(2R) * (R²/(R²+x²)^(3/2))
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Q. What is the magnetic field at the center of a circular loop of radius R carrying current I?
A.
μ₀I/2R
B.
μ₀I/R
C.
μ₀I/4R
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. What is the magnetic field at the center of a circular loop of radius R carrying a current I?
A.
μ₀I/(2R)
B.
μ₀I/(4R)
C.
μ₀I/(R)
D.
μ₀I/(8R)
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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. What is the magnetic field at the center of a square loop of side a carrying current I?
A.
μ₀I/4a
B.
μ₀I/2a
C.
μ₀I/a
D.
μ₀I/8a
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Solution
The magnetic field at the center of a square loop is B = μ₀I/4a.
Correct Answer: A — μ₀I/4a
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Q. What is the magnetic field at the midpoint of a wire carrying current I in opposite directions?
A.
Zero
B.
μ₀I/2
C.
μ₀I
D.
Depends on distance
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Solution
At the midpoint, the magnetic fields due to the two currents cancel each other out, resulting in zero net magnetic field.
Correct Answer: A — Zero
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Q. What is the magnetic field due to a circular loop of radius R carrying current I at a point on its axis at a distance x from the center?
A.
μ₀I/(2R)
B.
μ₀I/(2(x² + R²)^(3/2))
C.
μ₀I/(4πR)
D.
μ₀I/(x² + R²)
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Solution
The magnetic field at a point on the axis of a circular loop at a distance x from the center is given by B = μ₀I/(2(x² + R²)^(3/2)).
Correct Answer: B — μ₀I/(2(x² + R²)^(3/2))
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Q. What is the magnetic field due to a current I flowing through a straight wire at a distance d?
A.
μ₀I/(2πd)
B.
μ₀I/(4πd²)
C.
μ₀I/(d)
D.
μ₀I/(2d)
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Solution
The magnetic field B at a distance d from a straight wire carrying current I is given by B = μ₀I/(2πd).
Correct Answer: A — μ₀I/(2πd)
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Q. What is the magnetic field due to a current loop at a point on its axis?
A.
μ₀I/2R
B.
μ₀I/4R
C.
μ₀I/2R²
D.
μ₀I/4R²
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Solution
Using Ampere's Law, B = μ₀I/2R² at a point on the axis of a current loop.
Correct Answer: C — μ₀I/2R²
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Q. What is the magnetic field due to a long straight wire carrying current I at a distance r from the wire?
A.
μ₀I/2πr
B.
μ₀I/4πr
C.
μ₀I/πr
D.
μ₀I/8πr
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Solution
The magnetic field due to a long straight wire is given by B = (μ₀I)/(2πr).
Correct Answer: A — μ₀I/2πr
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Q. What is the magnetic field due to a magnetic dipole at a point along its axial line?
A.
(μ₀/4π) * (2m/r³)
B.
(μ₀/4π) * (m/r³)
C.
(μ₀/4π) * (m/r²)
D.
(μ₀/4π) * (m/r⁴)
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Solution
The magnetic field due to a magnetic dipole at a point along its axial line is given by B = (μ₀/4π) * (2m/r³).
Correct Answer: A — (μ₀/4π) * (2m/r³)
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Q. What is the magnetic field due to a solenoid of length L, carrying n turns per unit length and current I?
A.
μ₀nI
B.
μ₀nI/L
C.
μ₀nI/2
D.
μ₀nI/L²
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Solution
The magnetic field inside a long solenoid is B = μ₀nI.
Correct Answer: A — μ₀nI
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Q. What is the magnetic field due to a straight conductor at a point 1 meter away carrying a current of 5 A?
A.
0.01 T
B.
0.02 T
C.
0.03 T
D.
0.04 T
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Solution
Using Biot-Savart Law, B = μ₀I/(2πr) = (4π × 10^-7 Tm/A)(5 A)/(2π(1 m)) = 0.01 T.
Correct Answer: B — 0.02 T
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Q. What is the magnetic field due to a straight wire at a distance of 0.5 m carrying a current of 10 A?
A.
0.4 μT
B.
0.2 μT
C.
0.1 μT
D.
0.8 μT
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Solution
Using B = μ₀I/(2πr), substituting μ₀ = 4π × 10⁻⁷ Tm/A, I = 10 A, and r = 0.5 m gives B = 0.4 μT.
Correct Answer: A — 0.4 μT
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Q. What is the magnetic field inside a hollow conductor carrying current?
A.
Zero
B.
Uniform
C.
Varies with distance
D.
Depends on the current
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Solution
According to Ampere's law, the magnetic field inside a hollow conductor carrying current is zero.
Correct Answer: A — Zero
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Q. What is the magnetic field inside a hollow cylindrical shell carrying current I?
A.
0
B.
μ₀I/2πR
C.
μ₀I/4πR
D.
μ₀I/πR
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Solution
Inside a hollow cylindrical shell, the magnetic field is zero.
Correct Answer: A — 0
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Q. What is the magnetic field inside a long solenoid carrying current I?
A.
Zero
B.
μ₀nI
C.
μ₀I/n
D.
μ₀I/2
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Solution
The magnetic field inside a long solenoid is given by B = μ₀nI, where n is the number of turns per unit length.
Correct Answer: B — μ₀nI
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Q. What is the magnetic field inside a long solenoid carrying current?
A.
Zero
B.
Uniform and parallel to the axis
C.
Varies with distance
D.
Depends on the current only
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Solution
The magnetic field inside a long solenoid is uniform and parallel to the axis of the solenoid.
Correct Answer: B — Uniform and parallel to the axis
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Q. What is the magnetic field inside a long solenoid with n turns per unit length carrying a current I?
A.
μ₀nI
B.
μ₀I/n
C.
μ₀I/2n
D.
μ₀I/4n
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Solution
The magnetic field inside a long solenoid is given by B = μ₀nI.
Correct Answer: A — μ₀nI
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Q. What is the magnetic field inside a long straight conductor carrying a current I?
A.
0
B.
μ₀I/2πr
C.
μ₀I/4πr
D.
μ₀I/πr
Show solution
Solution
Using Ampere's Law, B = μ₀I/2πr for a long straight conductor.
Correct Answer: B — μ₀I/2πr
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Q. What is the magnetic field inside a long straight conductor carrying current I?
A.
0
B.
μ₀I/2πr
C.
μ₀I/4πr
D.
μ₀I/πr
Show solution
Solution
Using Ampere's Law, B = μ₀I/2πr for a long straight conductor.
Correct Answer: B — μ₀I/2πr
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Q. What is the magnetic field inside a long, ideal solenoid carrying current I?
A.
Zero
B.
μ₀I
C.
μ₀I/n
D.
μ₀nI
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Solution
The magnetic field inside a long, ideal solenoid is given by B = μ₀nI, where n is the number of turns per unit length.
Correct Answer: D — μ₀nI
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Q. What is the magnetic field inside a long, ideal solenoid carrying current?
A.
Zero
B.
Uniform and parallel
C.
Concentric circles
D.
Decreasing
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Solution
The magnetic field inside a long, ideal solenoid is uniform and parallel to the axis of the solenoid.
Correct Answer: B — Uniform and parallel
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Q. What is the magnetic field inside a long, ideal solenoid with n turns per unit length carrying a current I?
A.
B = μ₀nI
B.
B = μ₀I/n
C.
B = nI/μ₀
D.
B = μ₀I
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Solution
The magnetic field inside an ideal solenoid is given by B = μ₀nI, where n is the number of turns per unit length.
Correct Answer: A — B = μ₀nI
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Q. What is the magnetic field inside a long, ideal solenoid?
A.
Zero
B.
Uniform and parallel
C.
Concentric circles
D.
Diverging lines
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Solution
The magnetic field inside a long, ideal solenoid is uniform and parallel.
Correct Answer: B — Uniform and parallel
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Q. What is the magnetic field inside a long, straight solenoid carrying current I?
A.
0
B.
μ₀I
C.
μ₀nI
D.
μ₀nI/2
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Solution
The magnetic field inside a long, straight solenoid is given by B = μ₀nI, where n is the number of turns per unit length and μ₀ is the permeability of free space.
Correct Answer: C — μ₀nI
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Q. What is the magnetic field inside a long, straight solenoid carrying current?
A.
Zero
B.
Uniform and parallel to the axis
C.
Varies with distance
D.
Concentric circles
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Solution
The magnetic field inside a long, straight solenoid is uniform and parallel to the axis of the solenoid, given by B = μ₀nI, where n is the number of turns per unit length.
Correct Answer: B — Uniform and parallel to the axis
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Q. What is the magnetic field inside a solenoid carrying current I with n turns per unit length?
A.
μ₀nI
B.
μ₀I/n
C.
μ₀I
D.
μ₀nI/2
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Solution
The magnetic field inside a long solenoid is given by B = μ₀nI.
Correct Answer: A — μ₀nI
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Q. What is the magnetic field strength at the center of a square loop of side a carrying a current I?
A.
(μ₀I)/(2a)
B.
(μ₀I)/(4a)
C.
(μ₀I)/(√2a)
D.
(μ₀I)/(8a)
Show solution
Solution
The magnetic field at the center of a square loop is given by B = (μ₀I)/(√2a).
Correct Answer: C — (μ₀I)/(√2a)
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