Inside a circular loop of wire carrying current, the magnetic field lines are uniform and parallel, indicating a uniform magnetic field.

The magnetic field lines around a circular loop of wire are concentric circles centered on the axis of the loop.

Inside the loop, the magnetic field lines are nearly uniform and parallel, indicating a strong and consistent magnetic field.

According to Faraday's law of electromagnetic induction, an increase in magnetic field through the loop induces an EMF in the loop.

According to Faraday's law of electromagnetic induction, the induced EMF is directly proportional to the rate of change of magnetic flux. If the magnetic field strength is doubled, the induced EMF will also double.

According to Faraday's law of electromagnetic induction, the induced EMF is proportional to the rate of change of magnetic flux. Increasing the area increases the flux, thus increasing the induced EMF.

Total score = 65 * n + 85. New average = (65n + 85) / (n + 1).

Total score = 75 * 30 = 2250. New total = 2250 - 75 + 90 = 2265. New average = 2265 / 30 = 75.5.

At 3:15, the hour hand is at 97.5 degrees and the minute hand is at 90 degrees. The angle is 97.5 - 90 = 7.5 degrees.

Inductive reactance Xl = 2πfL = 2π(50)(0.5) = 31.42 Ω.

Magnetic flux (Φ) = B × A × cos(θ). Here, B = 0.5 T, A = 0.1 m², and θ = 0° (cos(0) = 1). Thus, Φ = 0.5 T × 0.1 m² × 1 = 0.05 Wb.

Magnetic flux (Φ) = B × A × N = 0.5 T × 0.1 m² × 100 = 5 Wb.

According to Ohm's law, if the resistance increases while the induced EMF remains constant, the induced current will decrease.

According to Faraday's law of electromagnetic induction, a changing magnetic field induces an electromotive force (EMF) in the coil.

According to Faraday's law of electromagnetic induction, an increase in magnetic field strength induces a greater EMF.

Doubling the magnetic field strength will double the induced EMF, as it is directly proportional to the magnetic field strength.

According to Faraday's law of electromagnetic induction, the induced EMF in a coil is directly proportional to the rate of change of magnetic flux. Increasing the magnetic field strength increases the magnetic flux, thus increasing the induced EMF.

Magnetic flux Φ = B * A * N = 0.5 T * 0.01 m² * 100 = 0.5 Wb.

Using Faraday's law, EMF = -N * (dΦ/dt) = -100 * 0.5 = -50 V. The induced EMF is 50 V.

Induced EMF (ε) = -N(dB/dt) = -100 * (0.5 - 0.2)/2 = -15 V.

Using Faraday's law, EMF = -N * (ΔB/Δt) = -100 * ((1.5 - 0.5) / 2) = -100 * (1 / 2) = -50 V. The magnitude is 50 V.

Induced EMF = -N * (ΔB/Δt) = -100 * ((1.5 - 0.5)/2) = -100 * (1/2) = -50 V. The magnitude is 50 V.

Probability of getting no heads (all tails) = (1/2)^3 = 1/8. Therefore, probability of at least one head = 1 - 1/8 = 7/8.

The total moment of inertia is I_cylinder + I_sphere = (1/2 MR^2) + (2/5 MR^2) = (7/10) MR^2.

Concave lenses always produce virtual and upright images regardless of the object distance.

Using the lens formula, 1/f = 1/v - 1/u, we find v = 8 cm.

For a concave lens, the image formed is virtual and erect when the object is placed beyond the focal length.

For a concave lens, the image formed is virtual and erect when the object is placed at any distance.

Using the lens formula, the image distance is calculated to be -16.67 cm.

Using the mirror formula, 1/f = 1/v + 1/u, where f = -10 cm (concave mirror), u = -30 cm. Solving gives v = -15 cm, which means the image is formed 15 cm in front of the mirror.