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A metal sphere is kept on an insulting stands. A negatively charged rod is brought near it, then the sphere is earthed as shown. On removing the earthing, and taking the negatively charged rod away, what will be the nature of charge on the sphere? Give reason for your answer.

Concept: Ohm's Law
Solve the following question.
Using Kirchhoff’s rules, calculate the current through the 40 Ω and 20 Ω resistors in the following circuit.

Concept: Kirchhoff’s Laws
Answer the following question.
What is the end error in a meter bridge? How is it overcome? The resistances in the two arms of the metre bridge are R = Ω and S respectively. When the resistance S is shunted with equal resistance, the new balance length found to be 1.5 l1, where l2 is the initial balancing length. calculate the value of s.

Concept: Cells, EMF, and Internal Resistance
A conductor of length ‘l’ is rotated about one of its ends at a constant angular speed ‘ω’ in a plane perpendicular to a uniform magnetic field B. Plot graphs to show variations of the emf induced across the ends of the conductor with
- angular speed ω and
- length of the conductor l.
Concept: Cells, EMF, and Internal Resistance
A current of 0.8 A flows in a conductor of 40 Ω for 1 minute. The heat produced in the conductor will be ______.
Concept: Ohm's Law
A cell of emf E is connected across an external resistance R. When current 'I' is drawn from the cell, the potential difference across the electrodes of the cell drops to V. The internal resistance 'r' of the cell is ______.
Concept: Cells, EMF, and Internal Resistance
Define relaxation time.
Concept: Drift of Electrons and the Origin of Resistivity
Derive an expression for resistivity of a conductor in terms of the number density of charge carriers in the conductor and relaxation time.
Concept: Drift of Electrons and the Origin of Resistivity
Obtain an expression for the energy stored in a solenoid of self-inductance ‘L’ when the current through it grows from zero to ‘I’.
Concept: Solenoid
Find the condition under which the charged particles moving with different speeds in the presence of electric and magnetic field vectors can be used to select charged particles of a particular speed.
Concept: Motion in a Magnetic Field
Can a galvanometer as such be used for measuring the current? Explain.
Concept: Moving Coil Galvanometer
Sketch a schematic diagram depicting oscillating electric and magnetic fields of an em wave propagating along + z-direction ?
Concept: Motion in a Magnetic Field
Two long straight parallel conductors 'a' and 'b', carrying steady currents Ia and Ib are separated by a distance d. Write the magnitude and direction of the magnetic field produced by the conductor 'a' at the points along the conductor 'b'. If the currents are flowing in the same direction, what is the nature and magnitude of the force between the two conductors?
Concept: Force Between Two Parallel Currents (Ampere’s Law)
Show with the help of a diagram how the force between the two conductors would change when the currents in them flow in the opposite directions?
Concept: Motion in a Magnetic Field
Two infinitely large plane thin parallel sheets having surface charge densities σ1 and σ2 (σ1 > σ2) are shown in the figure. Write the magnitudes and directions of the net fields in the regions marked II and III.

Concept: Force Between Two Parallel Currents (Ampere’s Law)
The motion of copper plate is damped when it is allowed to oscillate between the two poles of a magnet. What is the cause of this damping?
Concept: Motion in a Magnetic Field
Figure shows two circuits each having a galvanometer and a battery of 3V.
When the galvanometers in each arrangement do not show any deflection, obtain the ratio R1/R2.

Concept: Moving Coil Galvanometer
Define mutual inductance between two long coaxial solenoids. Find out the expression for the mutual inductance of inner solenoid of length l having the radius r1 and the number of turns n1 per unit length due to the second outer solenoid of same length and r2 number of turns per unit length.
Concept: Solenoid
A rectangular loop of size l × b carrying a steady current I is placed in a uniform magnetic field `vecB`. Prove that the torque `vectau`acting on the loop is give by `vectau =vecm xx vecB,`where `vecm` is the magnetic moment of the loop.
Concept: Torque on a Rectangular Current Loop in a Uniform Magnetic Field
