Daily Olympiad: Physics - Magnetic Effects Current [20260512]

Challenge yourself with today's JEE Main practice! This test covers 'Magnetic Effects Current' for Physics (JEE Main - 11). Level: Hard | Duration: 45 mins.

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1. A long straight conductor carries a current I. Two points P and Q are located at perpendicular distances r and 2r from the conductor. What is the ratio of the magnetic field intensities at P and Q?

Solution
Correct: A
The magnetic field around a long straight conductor is given by B = μ₀I/(2πr). Since B ∝ 1/r, the ratio of magnetic field intensities at P (distance r) and Q (distance 2r) becomes B_P/B_Q = (μ₀I/(2πr)) / (μ₀I/(4πr)) = 2:1.

2. A charged particle enters a uniform magnetic field at an angle θ with its initial velocity. If the magnetic field is in the +x direction and the initial velocity has components in both +y and +z directions, what is the shape of its trajectory?

Solution
Correct: B
The particle's motion has two components: perpendicular and parallel to the magnetic field. The perpendicular component causes circular motion, while the parallel component remains unaffected. The combination of these motions results in a helical path.

3. A circular loop of radius R carries a current I. What is the magnetic field at the center of the loop if it has N turns?

Solution
Correct: C
For a single-turn loop, the magnetic field at the center is B = μ₀I/(2R). For N turns, the field is multiplied by N. Thus, B = μ₀NI/(2R).

4. A solenoid of length l and radius r has n turns per unit length. If a current I flows through it, what is the magnetic field inside the solenoid?

Solution
Correct: A
Inside a solenoid, the magnetic field is given by B = μ₀nI, where n is the number of turns per unit length. This derivation assumes a long solenoid where end effects are negligible.

5. Two parallel wires carry equal currents in opposite directions. The distance between them is d. At what distance from the first wire is the magnetic field zero?

Solution
Correct: A
The magnetic fields from the two wires cancel only at a point equidistant from both. Since the currents are in opposite directions, their fields oppose and cancel at a point midway between them.