Biot Savart Law
Q. According to the Biot-Savart Law, the magnetic field dB at a point due to a current element Idl is proportional to which of the following?
A.
Idl
B.
sin(θ)
C.
1/r^2
D.
Both Idl and sin(θ)
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Solution
The magnetic field dB is proportional to Idl and sin(θ), where θ is the angle between the current element and the line connecting the current element to the point of interest.
Correct Answer: D — Both Idl and sin(θ)
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Q. For a circular loop of radius R carrying a current I, what is the magnetic field at the center of the loop?
A.
B = μ₀I/(2R)
B.
B = μ₀I/(4R)
C.
B = μ₀I/(πR)
D.
B = μ₀I/(2πR)
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Solution
The magnetic field at the center of a circular loop of radius R carrying current I is given by B = μ₀I/(2πR).
Correct Answer: D — B = μ₀I/(2πR)
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Q. If a current-carrying wire is bent into a circular loop, what is the direction of the magnetic field at the center of the loop according to the Biot-Savart Law?
A.
Out of the plane of the loop
B.
Into the plane of the loop
C.
Clockwise
D.
Counterclockwise
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Solution
According to the right-hand rule applied to the Biot-Savart Law, the magnetic field at the center of a circular loop of current is directed out of the plane of the loop.
Correct Answer: A — Out of the plane of the loop
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Q. If a long straight wire carries a current I, what is the direction of the magnetic field at a point located directly above the wire?
A.
Towards the wire
B.
Away from the wire
C.
Clockwise around the wire
D.
Counterclockwise around the wire
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Solution
Using the right-hand rule, the magnetic field at a point directly above the wire is directed counterclockwise around the wire.
Correct Answer: D — Counterclockwise around the wire
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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 the Biot-Savart Law?
A.
μ₀I/(2πr)
B.
μ₀I/(4πr^2)
C.
μ₀I/(2r)
D.
μ₀I/(4πr)
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Solution
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 long straight wire carries a current I, what is the magnetic field B at a distance r from the wire?
A.
B = μ₀I/(2πr)
B.
B = μ₀I/(4πr^2)
C.
B = μ₀I/(2r)
D.
B = μ₀I/(πr^2)
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Solution
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 — B = μ₀I/(2πr)
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Q. If a long straight wire carries a current I, what is the magnetic field B at a distance r from the wire according to the Biot-Savart Law?
A.
B = (μ₀I)/(2πr)
B.
B = (μ₀I)/(4πr²)
C.
B = (μ₀I)/(r)
D.
B = (μ₀I)/(2r)
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Solution
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 — B = (μ₀I)/(2πr)
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Q. If a wire carrying current I is bent into a semicircular arc of radius R, what is the magnetic field at the center of the arc?
A.
μ₀I/(4R)
B.
μ₀I/(2R)
C.
μ₀I/(8R)
D.
μ₀I/(πR)
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Solution
The magnetic field at the center of a semicircular arc of radius R carrying current I is given by B = μ₀I/(4R).
Correct Answer: A — μ₀I/(4R)
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Q. If a wire is bent into a semicircular shape, what is the magnetic field at the center of the semicircle due to current I?
A.
μ₀I/(4R)
B.
μ₀I/(2R)
C.
μ₀I/(πR)
D.
μ₀I/(8R)
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Solution
The magnetic field at the center of a semicircular wire carrying current I is given by B = μ₀I/(4R) for the semicircle, which is half of the full circular loop.
Correct Answer: C — μ₀I/(πR)
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Q. If the angle between the current element and the line joining the current element to the point of interest is 90 degrees, what is the contribution of that current element to the magnetic field?
A.
Maximum
B.
Minimum
C.
Zero
D.
Undefined
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Solution
If the angle is 90 degrees, the sine of the angle is zero, resulting in zero contribution to the magnetic field from that current element.
Correct Answer: C — Zero
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Q. If the current in a circular loop is increased, what happens to the magnetic field at the center of the loop?
A.
It decreases
B.
It increases
C.
It remains the same
D.
It becomes zero
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Solution
According to the Biot-Savart Law, increasing the current in a circular loop increases the magnetic field at the center of the loop.
Correct Answer: B — It increases
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Q. If the current in a wire is doubled, how does the magnetic field at a point 5 cm away from the wire change?
A.
It doubles
B.
It quadruples
C.
It remains the same
D.
It halves
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Solution
According to Biot-Savart Law, the magnetic field is directly proportional to the current. Therefore, if the current is doubled, the magnetic field also 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?
A.
It remains the same
B.
It doubles
C.
It quadruples
D.
It halves
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Solution
According to the Biot-Savart Law, the magnetic field is directly proportional to the current, so if the current is doubled, the magnetic field also doubles.
Correct Answer: B — It doubles
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Q. If two parallel wires carry currents in the same direction, what is the nature of the force between them?
A.
Attractive
B.
Repulsive
C.
No force
D.
Depends on the distance
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Solution
Two parallel wires carrying currents in the same direction experience an attractive force between them.
Correct Answer: A — Attractive
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Q. In a circular loop of radius R carrying a current I, what is the magnetic field at the center of the loop according to the Biot-Savart Law?
A.
B = (μ₀I)/(2R)
B.
B = (μ₀I)/(4R)
C.
B = (μ₀I)/(R)
D.
B = (μ₀I)/(πR)
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Solution
The magnetic field at the center of a circular loop of radius R carrying current I is given by B = (μ₀I)/(2R).
Correct Answer: A — B = (μ₀I)/(2R)
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Q. In a circular loop of radius R carrying a current I, what is the magnetic field at the center of the loop?
A.
μ₀I/(2R)
B.
μ₀I/(4R)
C.
μ₀I/(2πR)
D.
μ₀I/(4πR)
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Solution
The magnetic field B at the center of a circular loop of radius R carrying current I is given by B = μ₀I/(2R).
Correct Answer: A — μ₀I/(2R)
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Q. In a situation where two parallel wires carry currents in the same direction, what is the nature of the force between them?
A.
Attractive
B.
Repulsive
C.
No force
D.
Depends on the distance
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Solution
Two parallel wires carrying currents in the same direction experience an attractive force between them.
Correct Answer: A — Attractive
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Q. In a solenoid carrying current, what is the magnetic field inside the solenoid?
A.
Zero
B.
μ₀nI
C.
μ₀I
D.
μ₀I/(2n)
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Solution
The magnetic field inside a solenoid carrying current is given by B = μ₀nI, where n is the number of turns per unit length.
Correct Answer: B — μ₀nI
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Q. In Biot-Savart Law, what does the term 'dL' represent?
A.
Element of current
B.
Element of length
C.
Element of magnetic field
D.
Element of charge
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Solution
In Biot-Savart Law, 'dL' represents an infinitesimal element of length along the current-carrying conductor.
Correct Answer: B — Element of length
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Q. In the Biot-Savart Law, what does the term 'dl' represent?
A.
The length of the wire segment
B.
The distance from the wire to the point of interest
C.
The current flowing through the wire
D.
The angle between the wire and the point
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Solution
'dl' represents the infinitesimal length of the wire segment that contributes to the magnetic field at a point.
Correct Answer: A — The length of the wire segment
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Q. In the context of the Biot-Savart Law, what does the symbol μ₀ represent?
A.
Electric permittivity
B.
Magnetic permeability of free space
C.
Magnetic field strength
D.
Electric field strength
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Solution
The symbol μ₀ represents the magnetic permeability of free space, which is a constant used in the Biot-Savart Law.
Correct Answer: B — Magnetic permeability of free space
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Q. In the context of the Biot-Savart Law, what does the term 'current element' refer to?
A.
A small segment of wire carrying current
B.
The total current in the wire
C.
The direction of current flow
D.
The magnetic field produced by the current
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Solution
A 'current element' refers to a small segment of wire carrying current, which contributes to the overall magnetic field.
Correct Answer: A — A small segment of wire carrying current
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Q. Using Biot-Savart Law, what is the magnetic field at the center of a circular loop of radius R carrying current I?
A.
μ₀I/(2R)
B.
μ₀I/(4R)
C.
μ₀I/(πR)
D.
μ₀I/(2πR)
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Solution
The magnetic field at the center of a circular loop of radius R carrying current I is given by B = μ₀I/(2R) and for a complete loop, it simplifies to B = μ₀I/(2πR).
Correct Answer: D — μ₀I/(2πR)
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Q. What does the Biot-Savart Law describe?
A.
The force between two charges
B.
The magnetic field generated by a steady current
C.
The electric field due to a point charge
D.
The potential energy of a system of charges
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Solution
The Biot-Savart Law describes the magnetic field generated by a steady current flowing through a conductor.
Correct Answer: B — The magnetic field generated by a steady current
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Q. What is the direction of the magnetic field produced by a current-carrying loop at its center?
A.
Perpendicular to the plane of the loop
B.
In the plane of the loop
C.
Radially outward from the loop
D.
Radially inward towards the loop
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Solution
The magnetic field produced by a current-carrying loop at its center is perpendicular to the plane of the loop, following the right-hand rule.
Correct Answer: A — Perpendicular to the plane of the loop
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Q. What is the direction of the magnetic field produced by a current-carrying wire according to the Biot-Savart Law?
A.
Along the wire
B.
Perpendicular to the wire and the current
C.
In the direction of the current
D.
Opposite to the direction of the current
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Solution
The direction of the magnetic field produced by a current-carrying wire is perpendicular to both the wire and the direction of the current.
Correct Answer: B — Perpendicular to the wire and the current
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Q. What is the direction of the magnetic field produced by a current-carrying wire according to the right-hand rule?
A.
Towards the wire
B.
Away from the wire
C.
Perpendicular to the wire in the direction of current
D.
Perpendicular to the wire in the opposite direction of current
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Solution
According to the right-hand rule, if you point your thumb in the direction of the current, your fingers curl in the direction of the magnetic field.
Correct Answer: C — Perpendicular to the wire in the direction of current
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Q. What is the effect of doubling the distance from a long straight wire on the magnetic field strength?
A.
It doubles the magnetic field strength
B.
It halves the magnetic field strength
C.
It quadruples the magnetic field strength
D.
It has no effect on the magnetic field strength
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Solution
According to the Biot-Savart Law, the magnetic field strength is inversely proportional to the distance, so doubling the distance halves the magnetic field strength.
Correct Answer: B — It halves the magnetic field strength
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Q. What is the effect of increasing the current in a wire on the magnetic field around it?
A.
Increases the magnetic field
B.
Decreases the magnetic field
C.
No effect on the magnetic field
D.
Reverses the direction of the magnetic field
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Solution
Increasing the current in a wire increases the magnetic field around it, as per the Biot-Savart Law.
Correct Answer: A — Increases the magnetic field
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Q. What is the effect of increasing the distance from a current-carrying wire on the magnetic field strength?
A.
It increases
B.
It decreases
C.
It remains constant
D.
It becomes zero
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Solution
According to the Biot-Savart Law, the magnetic field strength decreases with increasing distance from the current-carrying wire.
Correct Answer: B — It decreases
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