Electrostatics

Step 1: Torque on a magnetic dipole in a magnetic field is where is the angle between and .
Step 2: Torque is maximum when
Step 3: Potential energy of a magnetic dipole in a magnetic field is
Step 4: At ,
Step 5: Hence, when the torque is maximum, the potential energy is zero.

Step 1: Find the speed of the proton after acceleration through potential . For a proton:
Step 2: Radius of circular path in magnetic field:
Step 3: The proton travels an arc of a circle inside the field. From geometry (see figure), Here,

Step 1: From the figure, there are three capacitors formed by six plates. For plates of equal area, capacitances are proportional to .
Step 2: Using the given reference:
Step 3: The three gaps in the diagram are . Therefore individual capacitances:
Step 4: These are in parallel between A and B: Hence → (C).

Step 1: For heater, temperature increases with time.
Step 2: Metallic resistance increases with temperature:
Step 3: Therefore current gradually decreases, not increases.
Step 4: Option (A) showing decreasing current is correct.

Step 1: Convert all temperatures to the same scale (Celsius). Step 2: Convert to Celsius. Step 3: Convert to Celsius. Step 4: Write the remaining values in Celsius. Step 5: Compare all temperatures in Celsius. The highest temperature (closest to zero) is: But among the converted values: Comparing all options correctly: However, option (B) corresponds to , which is lower than . Thus, re-check: Highest = Final Answer:

Step 1: Recall the normal temperature of the human body. Normal human body temperature is approximately: Step 2: Check equality of numerical values between different scales.

Fahrenheit and Celsius: They are numerically equal only at , not at body temperature.
Celsius and Kelvin: So numerical equality is impossible.
Kelvin and Reaumur: No numerical equality occurs at body temperature.
Step 3: Final conclusion. None of the given pairs have equal numerical values for the temperature of the human body.