two charges x axis 12 hc and 45 c and the third unknown charge are located o the located 12 mc c

Step 1:** Calculate the value of (x) by setting up the equation (frac{x}{(15+x)^2} = frac{4

Two charges x axis 12 hc and 45 c and the third unknown...

Two charges, X-axis. 12 C and 45 C; and the third unknown charge are located on the x-axis. The 12 C charge is located at the origin and the 45 C charge is at x = 15 cm. The unknown charge is to be placed so that each charge is in equilibrium under the action of the electric forces exerted by the other two. Find the required location, magnitude, and sign of the unknown charge.

Transcript

00:01 Hello students in this question we are given that there are two charges of minus 12 microculum so we have here charge 1 q1 which is minus 12 microculum and if it is located at origin q1 at origin the second charge q2 is 45 microculum and this is located at x equal to 15 centimeter and it is given that all the three charges are on x -axis and the unknown charge should be placed so that each charge is in equilibrium under the action of electric forces exerted by the other two charges so we have to find the required location magnitude and sign of the unknown charge so let here let third charge be placed third charge be placed at point p point p whose coordinate is minus x comma 0 so let us see the diagram so this is the diagram this is q1 at origin q2 at 15 .0 and we have at point p q3 whose coordinates is minus x .0 now since we want this charge such that the whole system is in equilibrium this means that summation of forces will be equal to 0 now we find out that force on charge 1 so that will be equal to.

01:42 So here we have force on charge q3 due to q1.

01:47 So force on charge 3 due to 2 will be equal in magnitude with force on charge 3 due to charge 1.

01:59 So they will be equal in magnitude.

02:04 Force on charge 3 due to charge 2 will be k q.

02:09 Q2 over the distance is this much as x and this is 15 so it is 15 plus x whole square now force on charge 3 due to charge 1 is k q1 q3 over x square so from here we have k and k gets cancelled q3 and q3 gets cancelled so we have x over 15 plus x whole square is equal to q2 over q1.

02:45 So from here we have x over 15 plus x whole square is equal to q2 is 45 microculum.

02:57 So this is 45 multiplied by 10 to the minus x over this is 12 microculum.

03:01 So 12 multiplied by 10 to the 1 minus x.

03:05 So here we have x over 15 plus x whole square.

03:11 Is equal to 45 over 12 and if we try to find out the value of x from here so we get the value of x approximately equal to 16 centimeter it means that at location minus 16 0 3rd charge should be placed and sign of charge can be either positive or negative so and we have to we have found the location and sign can be either so sign or of third charge can be positive or negative or negative.

03:59 Now we have to find the magnitude.

04:02 Now in order to find the magnitude of q3, we will balance the forces on q1...

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