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A cycle wheel of radius $0.5 \text{ m}$ is rotated with a constant angular velocity of $10 \text{ rad/s}$ in a region of a magnetic field of $0.1 \text{ T}$ which is perpendicular to the plane of the wheel. The EMF generated between its centre and the rim is:
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 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
What is the flux through a cube of side 'a' if a point charge q is at one of its corners?
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:
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:
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:
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:
Two pith balls carrying equal charges are suspended from a common point by strings of equal length, the equilibrium separation between them is r (as shown in Fig. I). Now, as shown in Fig. II, the strings are rigidly clamped at half the height. The equilibrium separation between the balls now becomes:
An inductor coil of self-inductance $10 \text{ H}$ carries a current of $1 \text{ A}$. The magnetic field energy stored in the coil is:
A uniform magnetic field is restricted within a region of radius $r$. The magnetic field changes with time at a rate $\frac{dB}{dt}$. Loop 1 of radius $R$ ($R > r$) encloses the region $r$ and Loop 2 of radius $R$ is entirely outside the region of the magnetic field as shown in the figure. Then the electromotive force (emf) generated is:
A 800 turn coil of effective area $0.05 \text{ m}^2$ is kept perpendicular to a magnetic field $5 \times 10^{-5} \text{ T}$. When the plane of the coil is rotated by $90^\circ$ around any of its coplanar axis in $0.1 \text{ s}$, the emf induced in the coil will be:
Two conducting circular loops of radii $R_1$ and $R_2$ are placed in the same plane with their centres coinciding. If $R_1 \gg R_2$, the mutual inductance $M$ between them will be directly proportional to:
A car sometimes overturns while taking a turn. When it overturns, it is:
Match List-I with List-II (the symbols carry their usual meaning). **List-I** (A) $\oint \vec{E} \cdot d\vec{A} = \frac{Q}{\varepsilon_0}$ (B) $\oint \vec{B} \cdot d\vec{A} = 0$ (C) $\oint \vec{E} \cdot d\vec{l} = -\frac{d\phi}{dt}$ (D) $\oint \vec{B} \cdot d\vec{l} = \mu_0 i_c + \mu_0 \varepsilon_0 \frac{d\phi_E}{dt}$ **List-II** (I) Ampere-Maxwell's law (II) Faraday's law (III) Gauss's law of electrostatics (IV) Gauss's law of magnetism
A coil of self-inductance $L$ is connected in series with a bulb $B$ and an AC source. The brightness of the bulb decreases when: