Physics Syllabus (JEE Main)
Q. If the charge density of a non-uniform spherical charge distribution varies as ρ(r) = kr², what is the electric field at the center of the sphere?
A.
0
B.
k/3ε₀
C.
k/4ε₀
D.
k/2ε₀
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Solution
At the center of a non-uniform spherical charge distribution, the electric field is zero due to symmetry.
Correct Answer: A — 0
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Q. If the charge density of a spherical charge distribution increases linearly with radius, how does the electric field vary inside the sphere?
A.
Linearly with radius
B.
Quadratically with radius
C.
Inversely with radius
D.
Constant
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Solution
The electric field inside a non-uniform charge distribution varies quadratically with radius due to the increasing charge density.
Correct Answer: B — Quadratically with radius
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Q. If the charge inside a closed surface is doubled, what happens to the electric flux through the surface?
A.
It doubles
B.
It halves
C.
It remains the same
D.
It becomes zero
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Solution
According to Gauss's law, the electric flux is directly proportional to the enclosed charge, so it doubles.
Correct Answer: A — It doubles
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Q. If the charge on a capacitor is doubled while the voltage remains constant, what happens to the capacitance?
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
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Solution
Capacitance C = Q/V; if Q is doubled and V remains constant, C must halve.
Correct Answer: B — It halves
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Q. If the charge on a capacitor is doubled, what happens to the energy stored in it?
A.
It doubles
B.
It quadruples
C.
It remains the same
D.
It halves
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Solution
The energy stored in a capacitor is given by U = 1/2 * C * V^2. If the charge is doubled, the energy stored quadruples.
Correct Answer: B — It quadruples
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Q. If the circumference of a circle is measured as 31.4 cm with an error of 0.2 cm, what is the radius?
A.
5 cm
B.
4.5 cm
C.
5.0 cm
D.
6 cm
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Solution
Circumference = 2πr. Measured circumference = 31.4 cm. Thus, r = 31.4 / (2π) ≈ 5.0 cm.
Correct Answer: C — 5.0 cm
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Q. If the circumference of a circle is measured as 31.4 cm with an error of 0.2 cm, what is the percentage error?
A.
0.64%
B.
0.5%
C.
1%
D.
0.2%
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Solution
Percentage error = (Absolute error / Measured value) * 100 = (0.2 / 31.4) * 100 ≈ 0.64%.
Correct Answer: A — 0.64%
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Q. If the critical angle for a certain material is 30°, what is the refractive index of that material?
A.
1.00
B.
1.15
C.
1.73
D.
2.00
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Solution
The refractive index n can be calculated using n = 1/sin(θc). For θc = 30°, n = 1/sin(30°) = 1/0.5 = 2.00.
Correct Answer: C — 1.73
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Q. If the critical angle for a certain material is 45°, what is the refractive index of that material?
A.
1.41
B.
1.00
C.
1.73
D.
0.71
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Solution
Using the formula n = 1/sin(θc), where θc = 45°, we find n = 1/sin(45°) = 1/0.7071 ≈ 1.41.
Correct Answer: A — 1.41
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Q. If the cross-sectional area of a wire is doubled, how does its resistance change?
A.
Doubles
B.
Halves
C.
Remains the same
D.
Increases four times
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Solution
Resistance is inversely proportional to cross-sectional area; doubling the area halves the resistance.
Correct Answer: B — Halves
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Q. If the cross-sectional area of a wire is doubled, what happens to its resistance?
A.
Doubles
B.
Halves
C.
Remains the same
D.
Increases four times
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Solution
Resistance (R) is inversely proportional to cross-sectional area (A). Doubling A halves the resistance.
Correct Answer: B — Halves
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Q. If the current in a circuit is 5 A and the resistance is 2 ohms, what is the power consumed in the circuit?
A.
10 W
B.
25 W
C.
5 W
D.
2.5 W
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Solution
Power (P) can be calculated using P = I^2R = (5 A)^2 * 2 Ω = 25 W.
Correct Answer: B — 25 W
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Q. If the current in a circuit is doubled while the resistance remains constant, what happens to the voltage?
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
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Solution
According to Ohm's Law, if the current (I) is doubled and resistance (R) remains constant, the voltage (V) must also double.
Correct Answer: A — It doubles
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Q. If the current in a circuit is halved, what happens to the power consumed by the circuit?
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
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Solution
Power P = I^2 * R. If I is halved, P becomes (1/2)^2 * R = 1/4 * P, so the power is reduced to a quarter, which means it halves.
Correct Answer: B — It halves
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Q. If the current in a circuit is split into two branches with resistances R1 = 2Ω and R2 = 4Ω, what is the current through R1 if the total current is 6A?
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Solution
Using the current division rule, I1 = I_total * (R2 / (R1 + R2)) = 6A * (4Ω / (2Ω + 4Ω)) = 6A * (4/6) = 4A.
Correct Answer: B — 3A
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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 circular loop is doubled, what happens to the magnetic field at the center?
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 the loop is directly proportional to the current.
Correct Answer: A — It doubles
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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 circular loop is reversed, what happens to the direction of the magnetic field at the center of the loop?
A.
It remains the same
B.
It reverses
C.
It doubles
D.
It becomes zero
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Solution
Reversing the current in a circular loop reverses the direction of the magnetic field at the center.
Correct Answer: B — It reverses
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Q. If the current in a coil is doubled, the magnetic field strength around the coil will?
A.
Double
B.
Halve
C.
Remain the same
D.
Increase by four times
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Solution
The magnetic field strength around a coil is directly proportional to the current, so if the current is doubled, the magnetic field strength will also double.
Correct Answer: A — Double
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Q. If the current in a coil is reversed, what happens to the direction of the magnetic field produced by the coil?
A.
It remains the same
B.
It reverses
C.
It increases
D.
It decreases
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Solution
Reversing the current in a coil reverses the direction of the magnetic field produced.
Correct Answer: B — It reverses
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Q. If the current in a solenoid is doubled, what happens to the magnetic field inside the solenoid?
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
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Solution
The magnetic field inside a solenoid is directly proportional to the current.
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 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 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 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 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 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 current in a wire is reversed, what happens to the direction of the magnetic field around it?
A.
It remains the same
B.
It reverses
C.
It doubles
D.
It becomes zero
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Solution
Reversing the current in a wire also reverses the direction of the magnetic field around it.
Correct Answer: B — It reverses
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Q. If the current through a 10Ω resistor is 2A, what is the voltage across the resistor?
A.
5V
B.
10V
C.
20V
D.
30V
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Solution
Using Ohm's law, V = I * R = 2A * 10Ω = 20V.
Correct Answer: C — 20V
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