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Chapter 26: Q.75 (page 741)

In Problems 75 through 77, you are given the equation(s) used to solve a problem. For each of these, you are to: a. Write a realistic problem for which this is the correct equation (s). b. Finish the solution to the problem.

2azV/m=-dVdzwhereas a is a constant with units ofV/m2V(z=0)=10V.

Short Answer

Expert verified

(a) The electric field is given as 2az, where a is a constant and z is the distance, in meters. Find the potential if the potential at distance z = 0 is 10 V. "

(b). V(z)=10-az2

Step by step solution

01

Step 1. Given information

2azV/m=-dVdz, where a is a constant with units ofV/m2,V(z=0)=10V.

02

Step 1. Finding a realistic problem for part (a)

Part (a)

The electric field is given as 2az, where a is a constant and z is the distance, in meters. Find the potential if the potential at distance z=0 is 10 V. "

03

Step 3. Simplify for Part (b).

Part (b)

We know that the following holds true:

2az=-dVdz

We can separate and integrate on both sides, thus finding

∫dV=-∫2azdz

Which leaves us

V(z)=-az2+c

The integration constant can be found by knowing the initial condition.

V(0)=c=10

This means that the potential is given as a function of z as

localid="1649476813420" V(z)=10-az2.

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