question 384 please not sure where to start A charge +Q is fixed distance 3R/2 f

Question

question 384 please not sure where to start

A charge +Q is fixed distance 3R/2 from another fixed charge of-Q/2.The figure shows an imaginary sphere of radius R whose center is on the line joining the two charge and at distance R/2 from the negative charge. Prove that the electrical potential over this sphere is zero, if it is defined to be zero infinitely far from these charges.(Hint: Pick any point on the circle and show V=0. A long metal cylinder of radius R_1 is coaxial WITH A LONG, HOLLOW METAL CYLINDER OF RADIUS R_2. THE cylinders are insulated from each other and from the SURROUNDINGS. Show that the potential difference between the CYLINDERS (V_1-V_2) IS: (V_1-V_2)= Explain why the potential difference is the same if the outer cylinder has no net charge on it. If the outer cylinder is absolute potential O V and the inner cylinder is absolute potential + 100 V, what is the potential at a point mid-way between the two cylindrical surfaces if R_2 3R_1? (Hint: You could use the result in and from it find V_1 - V _2, where r is any radius.) diagram in Problem 384 shows an end view of two long, coaxial hollow cylinders. Prove that at any radius r between the cylinders, the potential is: Where V_1 and V_2 are the potentials at the inner and outer surfaces, and R_1 and R_2

Explanation / Answer

lambda;charge per unit length on each cylinder

Q=lambda*L on each cylinder

electricfield between two cylinders using gauss law

E*(2*pi*RL)=lambda*L/epsilon

E=lambda/2*pi*epsilon*R

ELECTRIC POTENTIAL BETWEEN TWO CYLINDERS

V=-INTEGRAL OF(E.dr)

take limits from R1 TO R2

V1-V2=lambda/2*pi*epsilon *(ln(R2/R1)

for c part substitute values in the given problem you will get

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