Magnetic effect of current practice · Mixed difficulty

Option A (While taking reading of tangent galvanometer, the plane of the coil must be set at right angles to the earth’s magnetic meridian) is not true because the plane of the coil must be set *parallel* to the Earth's magnetic meridian.

Option C (Can be in equilibrium in two orientations, one stable while the other is unstable) is correct because the torque can be zero in two orientations, corresponding to stable and unstable equilibrium.

Option B (Statement I is true but Statement II is false) is correct because Newton's third law requires considering momentum in the electromagnetic field, and Ampere's law is derived from Biot-Savart's law.

Option B is correct because the magnetic field at the center of the loop is calculated using the formula for the magnetic field on the axis of a circular loop, and then solving for the magnetic field at the center.

Option D ($d \vec{B}=\frac{\mu_0 i}{4 \pi}\left(\frac{d \vec{l} \times \vec{r}}{r^3}\right)$) is correct because it represents the Biot-Savart law in vector form.

Option D ($9{\mu _0}$) is correct because Ampere's law states that the line integral of the magnetic field around a closed loop is proportional to the enclosed current, and the net current is 4A + 2A + 3A = 9A.

Option C (Infinite) is correct because an ideal voltmeter should have infinite resistance to avoid drawing any current from the circuit it's measuring, thus not affecting the voltage being measured.

Option D (If both Assertion & Reason are false) is correct because the magnetic induction increases, and the torque is not always zero.

Option B is correct. Both the assertion and the reason are true, but the reason doesn't fully explain the assertion. The time period depends on mass and charge, not just mass.

The question is incomplete and does not provide enough information to determine the ratio of the magnetic field. The magnetic field inside a capacitor while charging is proportional to the radius. The ratio is B1/B2 = (r1/R) / 1 = (R/2)/R = 1/2 = 0.5 for r1=R/2 and r2=R. However, this is not one of the options. Assuming the question meant to ask for the ratio of magnetic field at r=R/2 to the magnetic field at the edge of the plate (r=R), then the magnetic field at r=R is B = (mu_0*I*r)/(2*pi*R²) for r<R and B = (mu_0*I)/(2*pi*r) for r>R. At r=R, B = (mu_0*I)/(2*pi*R). At r=R/2, B = (mu_0*I*(R/2))/(2*pi*R²) = (mu_0*I)/(4*pi*R). The ratio is (mu_0*I)/(4*pi*R) / (mu_0*I)/(2*pi*R) = 1/2 = 0.5. Still not in the options. The question likely has an error.

Option D ($2:1$) is correct because the period of a charged particle in a magnetic field is proportional to its mass and inversely proportional to its charge, and an alpha particle has twice the charge and four times the mass of a proton.

Option B is correct because the time taken to travel a certain distance under uniform acceleration is inversely proportional to the square root of the acceleration, which is proportional to the charge-to-mass ratio.

Option D ($\frac{3}{2}$) is correct because the magnetic field is proportional to the current and the direction of the current affects the sign of the field.

Option D ($10 \Omega$) is correct because it is calculated using the formula for shunting an ammeter to increase its range.

Option A is correct because the assertion and reason are both true, and the reason accurately explains why the point charge experiences a force due to the induced charge on the conducting surface.

Option A ($\frac{\mu_0}{4 \pi} \frac{i_1 i_2}{d}$) is correct because the force per unit length between two parallel current-carrying conductors is directly proportional to the product of the currents and inversely proportional to the distance between them.

Option C (${10^{ - 19}}{\mu _0}$) is correct because it is the magnetic field calculated using the formula for the magnetic field at the center of a circular loop due to a moving charge.

Option A ($\frac{G}{49}$) is correct because it provides the correct shunt resistance to allow 2% of the main current to pass through the galvanometer.

Option C (Current) is correct because an ammeter is specifically designed to measure the electric current flowing through a circuit.

Option A (Quantity $v \times a$ is constant in time) is correct because the force is velocity-dependent, and the cross product of velocity and acceleration remains constant.

Option A (electric and magnetic fields) is correct because a moving electric charge generates both electric and magnetic fields.

Option B ($\mu_0 \times 10^{-19} \mathrm{~T}$) is correct because it is the magnetic field calculated at the center of the circle using the given radius, time, and charge of the helium nucleus.

Option D (Infinite) is correct because an ideal voltmeter should have infinite resistance to avoid drawing any current from the circuit being measured.

Option C is correct because when a charged particle enters a uniform magnetic field at an acute angle, its path becomes a helix with a uniform pitch due to the combined effect of circular and linear motion.

Option B ($B \propto r$) is correct because, inside the wire, the magnetic field increases linearly with the distance from the center.

Option B (Gauss law) is correct because Ampere's law relates the integral of the magnetic field around a closed loop to the current passing through the loop, similar to how Gauss's law relates the electric flux through a closed surface to the enclosed charge.

Option B (10 cm) is correct because the radius is calculated by using the formula for the magnetic field on the axis of a circular coil and setting up a ratio.

Option A (5T along +Y axis) is incorrect. The correct answer is D (0.2 T along +Y axis). The magnetic field is calculated by equating the electric and magnetic forces and solving for B.

Option A is correct. Statement I, II, and III are all true regarding the behavior of electrons in electric and magnetic fields and the forces on current-carrying wires.

Option B is correct because the radius of the coil is calculated by setting up a ratio of the magnetic fields at two points on the axis of the coil using the formula for the magnetic field on the axis.