Magnetic effect of current practice · Mixed difficulty

Option B is correct because the magnetic field due to a current element is maximum when the angle between the current element and the position vector is 90 degrees.

Option A (3) is correct because the acceleration and magnetic field are perpendicular, implying their dot product is zero.

Option B (Uniformly accelerated motion) is correct because the magnetic force provides centripetal acceleration, causing the charge to move in a circle with constant speed but changing velocity direction.

Option D is correct because when a charged particle enters a uniform magnetic field at an angle, its path becomes helical due to the combined effects of the magnetic force and the particle's velocity components.

The correct answer is D (it can go undeflected also) because if the electric and magnetic forces are balanced, the electron will experience no net force and continue in a straight line.

Option A (16) is correct because the focal length is calculated using the lens formula and the condition that the images are in the same plane.

Option D (A rectangular loop in a plane containing the axis of the solenoid, the loop being partly inside the solenoid, and partly outside it) is correct because this configuration allows for the application of Ampere's law to relate the magnetic field to the current.

Option D (28 GHz) is correct because it calculates the cyclotron frequency using the formula $f = \frac{{Bq}}{{2\pi m}}$ with the given magnetic field and electron properties.

Option A ($60 \mu \mathrm{A}$) is correct because the current is directly proportional to the deflection angle in a moving coil galvanometer.

Option C ($\frac{{1}}{{\mathrm{{r}}}}$) is correct because the magnetic field due to an infinitely long straight conductor is inversely proportional to the distance r.

Option D (while passing through a given place, the path of electron remains straight line. It can be definitely said that the magnetic field is not present at that place) is the wrong statement because the electron could be moving parallel to the magnetic field.

Option C (250 $\Omega$) is correct because the resistance is calculated by dividing the voltage sensitivity by the current sensitivity.

Option B (1:2) is correct because the radius of the trajectory is proportional to the mass and inversely proportional to the charge, leading to the ratio 1:2.

The correct answer is D (r²) because the magnetic moment is directly proportional to the area of the coil, which is proportional to r².

Option D ($\mathrm{0}\mathrm{.099}$) is correct because it is the shunt resistance value needed to convert the galvanometer into an ammeter of the specified range.

Option C (Both I and II) is correct because the magnetic moment is proportional to the area of the loop, and doubling the radius makes the area four times larger.

Option A (5) is incorrect. Option B (15) is incorrect. Option C (20) is incorrect. Option D (25) is correct because the neutral point is located at a distance where the magnetic fields due to both wires cancel each other out. The distance from the smaller current wire is calculated, then added to the distance between the wires to find the distance from the 1A wire.

Option C (Statement-I is false and statement-II is true) is correct because a man in a lift moving with uniform velocity will feel his normal weight, and in downward accelerated motion, the apparent weight decreases.

Option C (3) is correct because it is the length of the resistance wire calculated using the shunt resistance formula for converting a galvanometer into an ammeter.

Option C ($\frac{{2 \sqrt{2} \mu_0 \mathrm{i}}}{{\pi \mathrm{a}}}$) is correct because the magnetic field at the center of the square is the sum of the fields due to each side, calculated using the Biot-Savart law.

Option A ($1.6 \times 10^{-14} \mathrm{~N}$) is correct because it is calculated using the Lorentz force formula, considering the electron's charge, velocity, and the magnetic field strength.

Option D (vector, scalar) is correct because magnetic field is a vector quantity and electric field is a scalar quantity.

Option A ($-6.22 \times 10^7 \mathrm{~J} \mathrm{~kg}^{-1}$) is correct because it is the gravitational potential calculated using the given values for radius, density, and gravitational constant.

Option C (45) is correct because the error in a tangent galvanometer is minimized when the deflection is around 45 degrees.

Option C ($2.0 {~A}$) is correct because it's the current required to demagnetize the magnet, calculated using the coercivity and number of turns per unit length.

Option C ($250\,\mu T$) is correct because the magnetic field at the center of the loop is calculated using the formula and the given magnetic field at a point on the axis.

Option A ($\frac{\mu_0}{4 \pi} \frac{\mathrm{d} l \times \overrightarrow{\mathrm{r}}}{\mathrm{r}^3}$) is correct because it represents the Biot-Savart law in vector form, showing the relationship between the magnetic field, current element, and position vector.

Option A ((A) and (R) are true and (R) is the correct explanation of (A)) is correct because the net force is zero due to equal and opposite forces on opposite sides of the coil.