## Udit Gupta is teaching live on Unacademy Plus

Important Questions Udit Gupta Alumnus MNNIT Allahabad Ex-VMC Faculty of physics

Question 1 Two identical charged spheres are suspended in air from the same point by strings of equal length. The strings make an angle of 300 with vertical When suspended in a liquid of density 800 kg/m3, the angle remains same. If the density of material of sphere is 1600 kg/m3, the dielectric constant of the liquid is? (a) 1 (b) 2 (c) 3 (d) 4

Approach I hope you can imagine these two figures by reading the question. The difference in both is that in one case they are immersed in air, and in other, a liquid. But the angle remains same. This brings us to the point that electric force would change, hence if the angle has to remain same there must be change in some other force. 'IMMERSED'='BUO YANCY, FBD should do the job now.

Solution In ai Tsine F Tcose mg F mgtane In liquid Tsing F B +T'cose mg ir mg 2 mg Liquid

Solution F mg mg - B dVg 1600 2 d_ 1600-800

Question2 Two positive point charges a distance b apart have a total charge Q. For what values of charges, is the Coulomb force between them maximum? (a) Q,0 2 Q (b) 2'2 Q 30 (d) Need more information

Approach We can assume some charge (x) on one and remaining on the other (Q-x) Coulomb's force can be given as x(Q-x) This force is dependent on x. To maximize this force we can use either quadratic equation or calculus Mathematics. Physics here is done.

Solution x(Q-x) for maximum FO 0 'dx 2 Correct option is (b).

Solution By quadratic equation method, Assume q1 and q2 to be the charges on the bodies (q1+q2)2-(q1-q2)2 Q2-(q1-q2)2 1 + q2 Q. To maximize q1q2- Or,q1 = q2 = 2.