Magnetic effect of current practice · Mixed difficulty

Option B ($\frac{{qvR}}{2}$) is correct because the magnetic moment is directly proportional to the charge, velocity, and radius, and inversely proportional to 2.

The correct answer is C (The path of the particle may be $y^2+z^2=25$) because the magnetic force does no work, so the speed remains constant, and the motion is in the x-y plane.

Option D ($4.9 \times 10^{-5} \mathrm{~T}$) is correct because it is the minimum magnetic field required to balance the weight of the wire, calculated using $Mg = ilB$.

The correct answer is A (The particle is moving and magnetic field is perpendicular to the velocity) because the magnetic force is proportional to $q(v \times B)$.

Option C (right-hand thumb rule for both up and down currents) is correct because the right-hand thumb rule describes the direction of magnetic field lines around a current-carrying wire, regardless of the current's direction.

Option B ($\mathrm{q} \overrightarrow{\mathrm{E}}+\mathrm{q}(\overrightarrow{\mathrm{V}} \times \overrightarrow{\mathrm{B}})$) is correct because it represents the Lorentz force, which is the sum of the electric and magnetic forces on a moving charge.

Option B (Current) is correct because a tangent galvanometer is specifically designed to measure electric current based on the tangent law.

Option A ($\frac{\mu_0 \mathrm{I}}{2 \mathrm{r}}$) is correct because the magnetic field at the center of a current loop is given by this formula.

Option A is correct because the magnetic field due to the straight current-carrying conductor is parallel to the plane of the loop, resulting in zero force on the loop.

Option B ($i \propto \theta$) is correct because in a moving coil galvanometer, the deflection of the coil is directly proportional to the electric current passing through it.

Option C (28.1) is correct because the time elapsed is half the period of the circular motion of the electron in the magnetic field.

Option D (half) is correct because the deflection in a moving coil galvanometer is directly proportional to the number of turns.

Option C (High resistance in series in series with its coil) is correct because a voltmeter needs high resistance to minimize current drawn from the circuit being measured, achieved by adding a high resistance in series with the galvanometer coil.

Option C ((n-1)G) is correct because the series resistance required to increase the range of a voltmeter is (n-1)G, where G is the original resistance and n is the factor by which the range is increased.

Option D ($q \vec{E}+q(\vec{v} \times \vec{B})$) is correct because it represents the Lorentz force, which is the sum of the electric and magnetic forces on a moving charge.

Option C ($\frac{1}{\mathrm{x}^3}$) is correct because the magnetic field due to a current loop at a large distance varies inversely with the cube of the distance.

Statement A is incorrect because neutrons are uncharged and do not experience a force in a magnetic field. Statement B is correct because the period of revolution is directly proportional to mass.

Option B is correct because when a charged particle moves perpendicular to a magnetic field, its speed remains unchanged, only the direction changes.

Option D (K) is correct because the kinetic energy of the proton remains constant as the magnetic field changes, given the radius adjusts accordingly.

Option B (maximum, if $\overrightarrow{\mathrm{v}}$ perpendicular to $\overrightarrow{\mathrm{B}}$) is correct because the magnetic force is proportional to the sine of the angle between velocity and magnetic field, which is maximum at 90 degrees.

Option C is correct because the work done by a magnetic field on a moving charge is always zero, as the magnetic force is perpendicular to the direction of motion.

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 D (Momentum changes) is correct because in a non-uniform magnetic field, the direction of the force on the charged particle changes, leading to a change in momentum, even if speed remains constant.

Option C (Magnetic field only) is correct because a current-carrying wire produces a magnetic field around it.

Option A ($\frac{{E^2}}{{2 B^2 V_0}}$) is correct because it represents the specific charge derived from equating electric and magnetic forces and using the kinetic energy gained from the potential difference.

Option D (All of these) is correct because the electron can maintain constant velocity if there are no fields, if it moves parallel to the magnetic field, or if electric and magnetic forces cancel each other.

Option A (9980) is correct because the series resistance needed to convert the galvanometer into a voltmeter is calculated using the formula R = G(n-1).

Option A (9) is incorrect. Option B (8) is incorrect. Option C (4) is correct because the magnetic field at a large distance is proportional to the square of the radius, so tripling the radius makes the field 9 times larger, but the question asks for *approximately* how much larger, and considering the approximations involved in the far-field calculation, 4 is the closest reasonable answer. Option D (3) is incorrect.

Option D is correct because as the magnet oscillates in and out of the coil, it induces a current in the coil, which causes the galvanometer to deflect left and right. The amplitude of the deflection decreases as the magnet's oscillations dampen due to energy loss.

Option A ($\frac{8}{3} \times 10^{-6}$) is correct because it is calculated using the formula for the magnetic field due to a straight conductor at a given distance.