Ch 1 Numericals
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AGARWAL’S PHYSICS RAVI AGARWAL (M.Sc.) – 9913650950 / 9374727052 [email protected] TIME: 1 hr CH . 1 (Numericals) MARKS: 24 1 Two electric charges having magnitude 8.0 μC and -2.0 μC are separated by 20 cm. Where should third charged be placed so that the resultant force acting on it is zero? 2 As shown in fig., a square having length a has electric charge distribution of surface charge density σ = σ o xy. Calculate the total electric charge on the square. The Cartesian coordinate system is shown in the fig. 3 Calculate the total electric flux linked with a circular disc of radius a, situated at a distance R from a point charge q. [ Hint: ∫ rdr /(R 2 +r 2 ) 3/2 = -1/(R 2 +r 2 ) 1/2 ] 4 The surface charge density of a very large surface is equal to -3 × 10 -6 C/m 2 . From what distance should an electron of 150 eV energy be projected towards the plane so that its velocity becomes zero on reaching the plane? Charge of an electron = 1.6 × 10 -19 C, 1eV = 1.6 × 10 -19 J, ε o = 9 × 10 -12 SI. 5 Three charges, q each, are placed on the vertices of and equilateral triangle. Find the resultant force on another charge 2q kept at its centroid. The distance of the centroid from the vertices is 1 m. 6 An electric dipole of moment is p is placed in a uniform electric field E. The dipole is rotated through a very small angle θ from equilibrium and is released. Prove that it executes angular simple harmonic motion with frequency, f = 1 2 π √ pE I . Here I is the moment of inertia of the dipole about an axis passing through its centre and perpendicular to the dipole axis. BEST FOR PHYSICS
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Transcript of Ch 1 Numericals
AGARWAL’S PHYSICS RAVI AGARWAL (M.Sc.) – 9913650950 / 9374727052
TIME: 1 hr CH . 1 (Numericals) MARKS: 24
1 Two electric charges having magnitude 8.0 μC and -2.0 μC are separated by 20 cm. Where should third charged be placed so that the resultant force acting on it is zero?2 As shown in fig., a square having length a has electric charge distribution of
surface charge density σ = σo xy. Calculate the total electric charge on the square. The Cartesian coordinate system is shown in the fig. 3 Calculate the total electric flux linked with a circular disc of radius a, situated at a distance R from a point charge q.
[ Hint: ∫rdr/(R2+r2)3/2 = -1/(R2+r2)1/2]4 The surface charge density of a very large surface is equal to -3 × 10-6 C/m2. From what distance should an electron of 150 eV energy be projected towards the plane so that its velocity becomes zero on reaching the
plane? Charge of an electron = 1.6 × 10-19 C, 1eV = 1.6 × 10-19 J, εo = 9 × 10-12 SI.5 Three charges, q each, are placed on the vertices of and equilateral triangle. Find the resultant force on another charge 2q kept at its centroid. The distance of the centroid from the vertices is 1 m. 6 An electric dipole of moment is p⃗ is placed in a uniform electric fieldE⃗. The dipole is rotated through a
very small angle θ from equilibrium and is released. Prove that it executes angular simple harmonic motion with frequency, f = 12π
√ pEI . Here I is the moment of inertia of the dipole about
an axis passing through its centre and perpendicular to the dipole axis. 7 Q amount of electric charge is uniformly distributed on a ring of radius r. A sphere of radius r is drawn in such a way that the center of the sphere lies on the surface of the ring. Calculate the electric flux associated with the surface of the sphere.
8 A charge of 4 × 10-8 C is uniformly distributed all over the surface of a sphere of radius 1 cm. Another hollow sphere of radius 5 cm is concentric with the smaller sphere. Find intensity of electric field at a distance
of 2 cm from the centre. K = 9 × 109 SI.
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