The resultant force at any vertex of equilatral triangle is F=2×14πε0×q2l2cos30°=3×14πε0×q2l2The distance of centroid from any of the vertices =d=23×l sin60°=33lLet at the centroid the charge q0 is placed, so for equilibrium of the charges 14πε0×9qq03l2=3×14πε0×q2l2or q0=q3

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Solve this GURU NANAK HIGHER SECONDARY SCHOOL COMPOUND RANCHI, JHARKHAND-834001 Assignment (Physics MI) 01. • Three point charges +q each are kept at the vertices Ofan equilateral triangle of side Detennine the magnitude and sign of the charge to be kept at its centroid so that the charges at the vertices remain in equilibrium. 02. A charged particle, of charge 2gC and mass I O milligram, moving With a velocity Of 1000m/ s enters 03. 04. 05. 06. 07. 09. 10. II. 12. 13. 14. 16. a uniform electric field Of strength 103 NC-I directed perpendicular to its direction.ofmoiion. Find the velocity and displacement, of the particle after 10s: A charge is distributed uniform over a ring Of a radius Obtain an expression for the electric intensity E at a point on the axis of the ring. Hence show that for points at large distances from the ring, it behaves like a point charge. An electric dipole, when held at 300 with respect to a uniform electric field Of 104 NC-I experiences a torque of 9x 10-26 Nm. Calculate dipole moment Of the dipole. Given a uniform electric field E = 5 x103iNC-t , find the flux of this field through a square Of on a side Whose plane is parallel to the Y-Z plane. What would be the flux through the same square if the plane makes a 300 angle with the X-axis? A spherical Gaussian surface enclose a charge of 8.85x10-8C. (i) Calculate the electric flux passing through the surface. (ii) If the radius Of the Gaussian surface is doubled, how would the A uniform electric field E for and É — C for are given. A rieh\ circular cylinder Of length I cm and radius r cm has its centre at the origin and its axis along the 8-axis. Find out the net outward flux. Using Gauss' s law write the expression for the net charge within the cylinder. A charge cf 17.7 xlO¯C is distributed-uniformly Over a large sheet Of area Caicuiaae tile electric field intensity at a distance of20cm from it in air. TWO point charges ql and qa are located at points and respectively. Find the electric field, due to both these charges, at the point plot a graph showing the variation of coulomb force (F) versus where r is the distance between the two charges Ofeach pair Ofcharges: (lgC,2HC) and (2gC,3gC). Interpret the grgphs obtaipeg. Calculate the distance between two protons Such that the electrical repulsive force between them is equal to the weight Of either. A charge q is placed at the centre of the line joining two equal charges Q. Show that the system Cf three charges will be in equilibrium if q = —Q / 4 Find the amount of work done in rotating an electric dipole, of dipole moment 3.2xlOOCm from its position of stable equilibrium, to the position Of unstable equilibrium, in a uniform electric field Of intensity 104 N 'C. An isolated sphere has a capacitance 50pF.(i) Calculate its radius. much charge should be placed on it to raise its potential to 104V? A capacitor of unknown capacitance is connected across a battery of V volts. The charge stored in it is 360gc . When potential across the capacitor is reduced by 120V, the charge stored in it becomes Calculate: (i) The potential V and the unknown capacitance C. (ii) What will be the charge stored in the capacitor, if the voltage applied has increased by 120V? TWO capacitors Of capacitances 3gF and 6gF are charges to potentials of 2V and SV respectively. These two charged capacitors are connected in series. Find the potential across each of the two capacitors now.

T h e r e s u l \tan t f o r c e a t a n y v e r t e x o f e q u i l a t r a l t r i a n g l e i s F = 2 \times \frac{1}{4 π ε_{0}} \times \frac{q^{2}}{l^{2}} \cos 30 ° = \sqrt{3} \times \frac{1}{4 π ε_{0}} \times \frac{q^{2}}{l^{2}} T h e d i s \tan c e o f c e n t r o i d f r o m a n y o f t h e v e r t i c e s = d = \frac{2}{3} \times l \sin 60 ° = \frac{\sqrt{3}}{3} l L e t a t t h e c e n t r o i d t h e c h a r g e q_{0} i s p l a c e d, s o f o r e q u i l i b r i u m o f t h e c h a r g e s \frac{1}{4 π ε_{0}} \times \frac{9 q q_{0}}{3 l^{2}} = \sqrt{3} \times \frac{1}{4 π ε_{0}} \times \frac{q^{2}}{l^{2}} o r q_{0} = \frac{q}{\sqrt{3}}

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