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A solid metallic sphere has a charge +3Q. Concentric with this sphere is a conducting spherical shell having charge –Q. The radius of the sphere is a and that of the spherical shell is b (b > a). What is the electric field at a distance R (a < R < b) from the centre?
The angular speed of a fly wheel moving with uniform angular acceleration changes from 1200 rpm to 3120 rpm in 16 seconds. The angular acceleration in $\text{rad/s}^2$ is
Figure shows a potentiometer with a cell of 2.0 V and internal resistance 0.40 Ω maintaining a potential drop across the resistor wire AB. A standard cell which maintains a constant emf of 1.02 V (for very moderate currents up to a few mA) gives a balance point at 67.3 cm length of the wire. To ensure very low currents drawn from the standard cell, a very high resistance of 600 kΩ is put in series with it, which is shorted close to the balance point. The standard cell is then replaced by a cell of unknown emf ε and the balance point found similarly, turns out to be at 82.3 cm length of the wire. The value of ε is:
A polythene piece rubbed with wool is found to have a negative charge of $3 \times 10^{-7}$ C. The transfer of mass from wool to polythene is:
The figure shows a 2.0 V potentiometer used for the determination of the internal resistance of a 1.5 V cell. The balance point of the cell in the open circuit is 76.3 cm. When a resistor of 9.5 Ω is used in the external circuit of the cell, the balance point shifts to 64.8 cm length of the potentiometer wire. The internal resistance of the cell is:
A force $F = 20 + 10y$ acts on a particle in y-direction where F is in newton and y in meter. Work done by this force to move the particle from $y = 0$ to $y = 1 \text{ m}$ is
A positively charged ball hangs from a silk thread. We put a positive test charge q₀ at a point and measure F/q₀, then it can be predicted that the electric field strength E
A rectangular, a square, a circular and an elliptical loop, all in the $(x-y)$ plane, are moving out of a uniform magnetic field with a constant velocity, $\vec{v} = v\hat{i}$. The magnetic field is directed along the negative $z$-axis direction. The induced emf, during the passage of these loops, out of the field region, will not remain constant for:
A long solenoid has 1000 turns. When a current of $4 \text{ A}$ flows through it, the magnetic flux linked with each turn of the solenoid is $4 \times 10^{-3} \text{ Wb}$. The self-inductance of the solenoid is:
What is the flux through a cube of side 'a' if a point charge q is at one of its corners?
The magnetic potential energy stored in a certain inductor is $25 \text{ mJ}$, when the current in the inductor is $60 \text{ mA}$. This inductor is of inductance:
A spherical conductor of radius 12 cm has a charge of $1.6 \times 10^{-7}$ C distributed uniformly on its surface. The electric field just outside the sphere is:
The electrostatic force on a small sphere of charge $0.4 \, \mu\text{C}$ due to another small sphere of charge $-0.8 \, \mu\text{C}$ in the air is $0.2 \, \text{N}$. The distance between the two spheres is:
An electron (mass m) with an initial velocity v = v₀î (v₀ > 0) is in an electric field E = -E₀î (E₀ = constant > 0). Its de Broglie wavelength at the time t is given by:
An electron falls from rest through a vertical distance h in a uniform and vertically upward-directed electric field E. The direction of the electric field is now reversed, keeping its magnitude the same. A proton is allowed to fall from rest through the same vertical distance h. The fall time of the electron in comparison to the fall time of the proton is:
Three point charges +q, -2q and +q are placed at points (x=0, y=a, z=0), (x=0, y=0, z=0) and (x=a, y=0, z=0) respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are:
A capacitor of capacitance $C$ is connected across an AC source of voltage $V$, given by; $V=V_0 \sin \omega t$. The displacement current between the plates of the capacitor would then be given by:
The current ($I$) in the inductance is varying with time ($t$) according to the plot shown in the figure. Which one of the following is the correct variation of voltage with time in the coil?
PQ is an infinite current carrying conductor carrying current $I$. AB and CD are smooth conducting rods on which a conductor EF moves with constant velocity $v$ as shown. The conductor EF is perpendicular to PQ and its ends are at distances $a$ and $b$ from the wire. The force needed to maintain constant speed of EF is:
A long solenoid has 500 turns. When a current of $2 \text{ A}$ is passed through it, the resulting magnetic flux linked with each turn of the solenoid is $4 \times 10^{-3} \text{ Wb}$. The self-inductance of the solenoid is: