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(i) A conductor A with a cavity as shown in Fig. is given a charge Q. Show that the entire charge must appear on the outer surface of the conductor.(ii) Another conductor B with charge q is inserted into the cavity keeping B insulated from A. Show that the total charge on the outside surface of A is Q + q [Fig.(b)].(iii) A sensitive instrument is to be shielded from the strong electrostatic fields in its environment. Suggest a possible

asked Mar 20, 2022 in 12th Physics by varun (6.7k points)

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A hollow charged conductor has a tiny hole cut into its surface. Show that the electric field in the hole is `(σ/2ε_0 )hatn` , where `hatn` is the unit vector in the outward normal direction, and σ is the surface charge density near the

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Obtain the formula for the electric field due to a long thin wire of uniform linear charge density E without using Gauss’s law. [Hint: Use Coulomb’s law directly and evaluate the necessary

asked Mar 20, 2022 in 12th Physics by varun (6.7k points)

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It is now believed that protons and neutrons (which constitute nuclei of ordinary matter) are themselves built out of more elementary units called quarks. A proton and a neutron consist of three quarks each. Two types of quarks, the so called ‘up’ quark (denoted by u) of charge + (2/3) e, and the ‘down’ quark (denoted by d) of charge (–1/3) e, together with electrons build up ordinary matter. (Quarks of other types have also been found which give rise to different unusual varieties of matter.) Suggest a possible quark composition of a proton and

asked Mar 20, 2022 in 12th Physics by varun (6.7k points)

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(i) Consider an arbitrary electrostatic field configuration. A small test charge is placed at a null point (i.e., where E = 0) of the configuration. Show that the equilibrium of the test charge is necessarily unstable.(ii) Verify this result for the simple configuration of two charges of the same magnitude and sign placed a certain distance

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A particle of mass m and charge (–q) enters the region between the two charged plates initially moving along x-axis with speed vx (like particle 1 in Fig. ). The length of plate is L and an uniform electric field E is maintained between the plates. Show that the vertical deflection of the particle at the far edge of the plate is `(qEL^2)/(2m v_x^2)`. Compare this motion with motion of a projectile in gravitational field discussed in Section 4.10 of Class XI Textbook of

asked Mar 20, 2022 in 12th Physics by varun (6.7k points)

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Two fixed, identical conducting plates (α & β ) , each of surface area S are charged to –Q and q, respectively, whereQ > q > 0. A third identical plate (γ ), free to move is located on the other side of the plate with charge q at a distance d (Fig ). The third plate is released and collides with the plate β . Assume the collision is elastic and the time of collision is sufficient to redistribute charge amongst β & γ . (i) Find the electric field acting on the plate γ before collision.(ii)

asked Mar 20, 2022 in 12th Physics by varun (6.7k points)

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There is another useful system of units, besides the SI/mks A system, called the cgs (centimeter-gram-second) system. In this system Coloumb’s law is given by`F=(Qq)/r^2 hatr` where the distance r is measured in cm (= 10–2 m), F in dynes (=10–5 N) and the charges in electrostatic units (es units), where 1es unit of charge =`1/[3] ×10^(-9)`The number [3] actually arises from the speed of light in vaccum which is now taken to be exactly given by c = 2.99792458 × 108 m/s. An approximate value of c then is c = [3] × 108 m/s. (i)

asked Mar 20, 2022 in 12th Physics by varun (6.7k points)

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Two charges –q each are fixed separated by distance 2d. A third charge q of mass m placed at the mid-point is displaced slightly by x (x << d) perpendicular to the line joining the two fixed charged as shown in Fig. . Show that q will perform simple harmonic oscillation of time period..

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Total charge –Q is uniformly spread along length of a ring of radius R. A small test charge +q of mass m is kept at the centre of the ring and is given a gentle push along the axis of the ring. (i) Show that the particle executes a simple harmonic oscillation.(ii) Obtain its time

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A positive charge Q is uniformly distributed along a circular ring of radius R. A small test charge q is placed at the centre of the ring as shown in then

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Fig. shows a long straight wire of a circular cross-section (radius a) carrying steady current I. The current I is uniformly distributed across this cross-section. Calculate the magnetic field in the region r < a and r >

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A 100 turn closely wound circular coil of radius 10 cm carries a current of 3.2 A.(i) What is the field at the centre of the coil?(ii) What is the magnetic moment of this coil? The coil is placed in a vertical plane and is free to rotate about a horizontal axis which coincides with its diameter. A uniform magnetic field of 2T in the horizontal direction exists such that initially the axis of the coil is in the direction of the field. The coil rotates through an angle of 90° under the influence of the magnetic field.(iii) What are

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For a circular coil of radius R and N turns carrying current I, the magnitude of the magnetic field at a point on its axis at a distance x from its centre is given by, B=`(mu_0IR^2N ) /(2(x^2+R^2)^(3/2))`(i) Show that this reduces to the familiar result for field at the centre of the coil.(ii) Consider two parallel co-axial circular coils of equal radius R, and number of turns N, carrying equal currents in the same direction, and separated by a distance R. Show that the field on the axis around the mid-point between the coils is uniform over a distance

asked Mar 20, 2022 in 12th Physics by varun (6.7k points)

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What is the focal length of a convex lens of focal length 30cm in contact with a concave lens of focal length 20cm? Is the system a converging or a diverging lens? Ignore thickness of the lenses. Determine the ‘effective focal length’ of the combination of the two

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What is the focal length of a convex lens of focal length 30cm in contact with a concave lens of focal length 20cm? An object 1.5 cm in size is placed on the side of the convex lens in the arrangement above. The distance between the object and

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A card sheet divided into squares each of size 1 mm2 is being viewed at a distance of 9 cm through a magnifying glass (a converging lens of focal length 9 cm) held close to the eye. What is the magnification produced by the lens? How much is the

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Figushows an equiconvex lens (of refractive index 1.50) in contact with a liquid layer on top of a plane mirror. A small needle with its tip on the principal axis is moved along the axis until its inverted image is found at the position of the needle. The distance of the needle from the lens is measured to be 45.0cm. The liquid is removed and the experiment is repeated. The new distance is measured to be 30.0cm. What is the refractive index of the

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(i) A point object O is kept in a medium of refractive index in front of a convex spherical surface of radius of curvature R which separates the second medium of refractive index `n_2` from the first one, as shown in the figure.Draw the ray diagram showing the image formation and deduce the relationship between the object distance and the image distance in terms of `n_1 , n_2 and R`.(ii) When the image formed above acts as a virtual object for a concave spherical surface separating the medium `n_2` from `n_1(n_2 > n_1)` , draw this ray diagram and write

asked Mar 20, 2022 in 12th Physics by varun (6.7k points)

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(i) A ray PQ of light is incident on the face AB of a glass prism ABC (as shown in the figure) and emerges out of the face AC. Trace the path of the ray. Show that `/_i+/_e=/_A+/_delta` where, `delta` and e denote the angle of deviation and angle of emergence respectively. Plot a graph showing the variation of the angle of deviation as a function of angle of incidence. State the condition under which `/_delta` is minimum. (ii) Find out the relation between the refractive index `(mu)` of the glass prism and `/_A` for the case, when the angle

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