The third charge must be placed between +q and -q, closer to -q to balance the forces.

The electric field is zero at a point closer to -q because the magnitudes of the fields due to both charges will be equal at that point.

The distance between the centers of two externally tangent circles is the sum of their radii: 3 + 4 = 7 cm.

Distance between centers = r1 + r2 = 3 cm + 5 cm = 8 cm.

The distance between the centers of two externally tangent circles is the sum of their radii: 3 + 4 = 7 cm.

Distance between centers = r1 + r2 = 5 cm + 3 cm = 8 cm.

Constructive interference occurs when the path difference is an integer multiple of λ.

A phase difference of π radians corresponds to a path difference of λ/2, leading to destructive interference.

Constructive interference occurs when the path difference is an integer multiple of λ, and 0.5λ corresponds to a half wavelength, leading to constructive interference.

Phase difference (Δφ) = (2π/λ) * path difference. For sound in air, λ = v/f. Assuming f = 1000 Hz and v = 340 m/s, λ = 0.34 m. Δφ = (2π/0.34) * 0.5 = π/2 rad.

Phase difference (φ) = (2π/λ) * path difference. Given λ = 1 m, φ = (2π/1) * 0.5 = π rad.

Relative speed = 12 + 15 = 27 km/h. Distance apart after 2 hours = 27 * 2 = 54 km.

Distance apart = (15 + 20) * 1 = 35 km.

Distance apart = (Speed of A + Speed of B) × Time = (12 km/h + 16 km/h) × 1.5 h = 42 km.

Relative speed = 15 km/h - 10 km/h = 5 km/h. Distance apart = Relative speed × Time = 5 km/h × 2 h = 10 km.

Relative speed = 15 km/h - 12 km/h = 3 km/h. Time = Distance / Speed = 9 km / 3 km/h = 3 hours.

Relative speed = 15 km/h - 12 km/h = 3 km/h. Distance apart = Relative speed × Time = 3 km/h × 2 h = 6 km.

Possible outcomes for sum = 7 are (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 outcomes. Total outcomes = 6 * 6 = 36. Probability = 6/36 = 1/6.

According to Coulomb's law, F ∝ 1/r². Reducing the distance to half increases the force by a factor of 4.

According to Coulomb's law, F ∝ q1 * q2. If both charges are doubled, the force becomes 4 times the original force.

Using Coulomb's law, F = k * |q1 * q2| / r². Let q be the charge, then 9 = (9 × 10^9) * (q²) / (1)². Solving gives q = 3μC.

U = k * q1 * q2 / r = (9 × 10^9) * (1 × 10^-6) * (1 × 10^-6) / 1 = 9 × 10^-3 J.

When brought into contact, the charges will redistribute equally, resulting in 0μC on each sphere.

When brought into contact, the charges will redistribute equally, resulting in 0μC on each sphere.

The electric fields due to both charges at the midpoint are equal and opposite, thus they cancel each other out, resulting in 0 N/C.

Potential energy U = k * q1 * q2 / r = (9 × 10^9 N m²/C²) * (5 × 10^-6 C)² / 1 m = 0.225 J.

When two identical spheres are brought into contact, they share their charges equally. Thus, they will have equal positive and negative charges after separation.

If two lines are perpendicular, the sum of their angles is 90 degrees. Therefore, if one line makes an angle of 30 degrees with the horizontal, the other line must make an angle of 90 - 30 = 60 degrees with the horizontal.

Perpendicular lines intersect at right angles, which measure 90 degrees.

Vertically opposite angles are equal. Therefore, the measure of the vertically opposite angle is also 70 degrees.