Question

This question focuses on reasoning about equilibrium inside the nickel block shown in Figure 14.92. Start with these premises:

• The definition of equilibrium inside a conductor and
• The relationship between average drift speed and electric field

in a conductor to reason about which situations are possibleinside the nickel block at equilibrium. Some of the situations listed below are possible, some are ruled out by one premise, and some are ruled out by two premises. If a situation is ruled out by two premises, choose both.

Case 1:\({\bf{\bar v = 0}}\)and \({{\bf{E}}_{{\bf{net}}}}{\bf{ = 0}}\) (1) Possible, (2) Not possible by definition of equilibrium, (3) Not possible because \({\bf{\bar v = u}}{{\bf{E}}_{{\bf{net}}}}\)

Case 2:\({\bf{\bar v = 0}}\)and \({{\bf{E}}_{{\bf{net}}}}{\bf{ > 0}}\) (1) Possible, (2) Not possible by definition of equilibrium, (3) Not possible because \({\bf{\bar v = u}}{{\bf{E}}_{{\bf{net}}}}\)

Case 3:\({\bf{\bar v > 0}}\)and \({{\bf{E}}_{{\bf{net}}}}{\bf{ = 0}}\) (1) Possible, (2) Not possible by definition of equilibrium, (3) Not possible because \({\bf{\bar v = u}}{{\bf{E}}_{{\bf{net}}}}\)

Case 4:\({\bf{\bar v > 0}}\)and \({{\bf{E}}_{{\bf{net}}}}{\bf{ > 0}}\) (1) Possible, (2) Not possible by definition of equilibrium, (3) Not possible because \({\bf{\bar v = u}}{{\bf{E}}_{{\bf{net}}}}\)

Now that you have considered each case, in equilibrium, which one is the only situation that is physically possible? (1) Case 1, (2) Case 2, (3) Case 3, (4) Case 4

Short answer

Case 1 is possible.

Case 2 is not possible by the definition of equilibrium.

Case 3 is not possible because\({\bf{\bar v = u}}{{\bf{E}}_{{\bf{net}}}}\).

Case 4 is not possible by definition of equilibrium and because\({\bf{\bar v = u}}{{\bf{E}}_{{\bf{net}}}}\).

Case 1 is the only situation that is physically possible.

Step-by-step solution

Given data

An uncharged nickel block is placed in an external electric field. The following cases are stated:

Case 1:\(\bar v = 0\) and\({E_{{\rm{net}}}} = 0\)

Case 2:\(\bar v = 0\)and\({E_{{\rm{net}}}} > 0\)

Case 3:\(\bar v > 0\)and\({E_{{\rm{net}}}} = 0\)

Case 4: \(\bar v > 0\) and \({E_{{\rm{net}}}} > 0\)

Electric field inside a conductor and drift velocity

At equilibrium the polarization field cancels out the external electric field and hence the net electric field inside a conductor is zero.

The drift velocity of mobile charges in a conductor is directly proportional to the applied electric field. The proportionality constant is called mobility.

Determination of the possibility of the mentioned cases

At equilibrium the net field inside a conductor is zero. Since the drift velocity is proportional to the net field, it is also zero inside the conductor. Hence Case 1 is possible.

Case 2 is impossible by the definition of equilibrium which states that the net field inside a conductor is zero.

Case 3 is impossible by the definition of drift velocity. Since the net field is zero inside the conductor, the draft velocity has to be zero too.

Case 4 is not possible both by the definition of equilibrium and that of drift velocity. At equilibrium the net field is zero inside the conductor and hence the drift velocity is zero too.