Magnetic effect of current practice · Mixed difficulty

Option D (All of these) is correct because the electron can pass undeflected if both E and B are zero, or if the electric and magnetic forces cancel each other out, or if the velocity is parallel to B when E is zero.

Option B ($\frac{{qvR}}{2}$) is correct because the magnetic moment is given by the product of the current and the area of the loop.

Option B (6 Cm) is correct because the conductor must be placed such that the forces from the other two wires balance out.

Option B is correct. The magnetic moment is related to the angular momentum by a negative sign due to the negative charge of the electron.

Option A is correct because the magnetic flux density is calculated using the formula B = (μ₀NI) / (2r).

Option A is correct because the kinetic energy remains constant as the magnetic force does no work on the particle, and the speed is unaffected.

Option C is correct because the magnetic fields from each wire add up constructively at the midpoint, and the formula for the magnetic field due to a long straight wire is used.

Option D (A helix with increasing pitch) is correct because the electric field accelerates the particle along the field direction, while the magnetic field causes it to move in a circle perpendicular to the field. The increasing velocity along the field leads to an increasing pitch.

Option C (High resistance in series) is correct because it converts the ammeter into a voltmeter by limiting the current and measuring the voltage drop across the resistance.

Option B ($1: 2$) is correct because the magnetic field at the center of a coil is proportional to the number of turns, so doubling the turns doubles the magnetic field.

Option C (-2F/3) is correct because the force is proportional to the product of the currents and inversely proportional to the distance between the wires.

Option A (Straight line) is correct because if the particle is at rest, the magnetic force is zero, and the electric force, being parallel to the electric field, will cause the particle to move in a straight line along the field.

Option C (The electric field may or may not be zero) is correct because if the electric and magnetic forces cancel each other, the net force can be zero even if both fields are non-zero. If both fields are zero, the net force is also zero.

Option B ($6.6 \times {10^{ - 5}}C/{m^3}$) is correct because it is calculated using the current density and the velocity of the protons.

Option C (Remain unchanged) is correct because the current through the tangent galvanometer remains the same even when the number of turns is doubled, due to the ideal battery.

Option C is correct. The cyclotron frequency is independent of the speed of the charged particle, depending only on the magnetic field and the charge-to-mass ratio.

Option C (Zero) is correct because the magnetic flux through the loop remains zero as the magnetic field is parallel to the plane of the loop.

Option A ($\mathrm{F}=\mathrm{i} l \mathrm{~B} \sin \theta$) is correct because it represents the magnitude of the force on a current-carrying conductor in a magnetic field.

Option C ($a$) is correct because the electric field is maximum at a distance equal to the radius divided by the square root of 2, which simplifies to a.

Option A (I) is correct because the magnetic field due to a long straight wire is directly proportional to the current I.

The correct answer is B (Current sensitivity of the galvanometer) because current sensitivity is defined as the deflection per unit current.

Option A ($\frac{{9{\mu _0}i}}{{4\pi L}}$) is correct because it is derived from calculating the magnetic field due to each side of the triangle and summing them up.

Option A (2) is correct because the magnetic field inside a solenoid is uniform and approximately twice the field at the end.

Option B (zero) is correct because according to Ampere's law, the magnetic field inside a current-carrying tube is zero due to symmetry and no enclosed current within the Amperian loop inside the tube.

Option D (High residence in series) is correct because adding a high resistance in series limits the current through the galvanometer, allowing it to measure voltage.

Option B (If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion) is correct. The assertion is true because the magnetic force is always perpendicular to the velocity, causing circular motion. The reason is also true, but it doesn't fully explain WHY the motion is circular (constant magnitude of velocity).

Option B ($F \propto \frac{1}{d}$) is correct because the force per unit length between two parallel wires is inversely proportional to the distance between them.

Option C (3) is correct because the length of the resistance wire is calculated using the shunt resistance formula and the specific resistance of the wire.

Option B (Planes of Helmholtz coils are perpendicular to each other) is correct because Helmholtz coils are coaxial, meaning their planes are parallel, not perpendicular.

Statement - 1 is True, Statement-2 is False. Soft iron has high permeability and is easily magnetized and demagnetized, making statement 2 false.