1.1 Quiz (Gradient of a Scalar Field)

1、单选题：
‌About gradient, which one is right?‍
选项：
A: Gradient of a scalar field is a scalar.
B: The magnitude of a gradient is the maximum change rate of the scalar function.
C: The direction of a gradient is the direction of the directional derivative.
D: The gradient of a constant is not certain.
答案: 【 The magnitude of a gradient is the maximum change rate of the scalar function.】

2、单选题：
​About the relationship between gradient and directional derivative of a scalar field, which one is right?‏
选项：
A: The magnitude of a gradient is the maximum value of the scalar function at the point, and its direction is the direction in which the scalar function changes the most slowly.
B: The magnitude of a gradient is the minimum change rate of the scalar function at this point, and its direction is the reverse direction of the maximum change of the scalar function.
C: The magnitude of a gradient is the maximum change rate of the scalar function at this point, and its direction is the direction in which the scalar function is increasing the most rapidly.
D: The magnitude of a gradient is the minimum value of the scalar function at this point, and its direction is the direction in which the scalar function is increasing the most rapidly.
答案: 【 The magnitude of a gradient is the maximum change rate of the scalar function at this point, and its direction is the direction in which the scalar function is increasing the most rapidly.】

3、单选题：
‎About gradient and directional derivative, which one is false?​
选项：
A: Along the direction of the gradient, change rate of the scalar is the maximum.
B: The directional derivative is the maximum in the direction of the gradient.
C: If the directional derivative is positive, the function increases in this direction.
D: The directional derivative of a scalar function at a given point is unique.
答案: 【 The directional derivative of a scalar function at a given point is unique.】

4、单选题：

​

‏选项：
A:
B:
C:
D:
答案: 【 】

5、单选题：

​

‎选项：
A:
B:
C:
D:
答案: 【 】

1.2 Quiz (Divergence of a Vector Field)

1、单选题：
‌Which one is false?‎
选项：
A: Divergence of a vector field is a scalar.
B: Divergence of a scalar field is a scalar.
C: If divergence of a vector field at one point is positive, there is a positive source at this point
D: If divergence of a vector field at one point is zero, there is no source at this point.
答案: 【 Divergence of a scalar field is a scalar.】

2、单选题：

‏

‌选项：
A:  1 
B:  2 
C:  3
D:  4
答案: 【  2 】

3、单选题：

​

‍选项：
A: 10
B: 8
C: 12
D: 14
答案: 【 8】

4、单选题：

​

‏选项：
A:
B:
C:
D:
答案: 【 】

1.3 Quiz (Curl of a Vector Field)

1、单选题：

​

‍选项：
A:
B:
C:
D:
答案: 【 】

2、单选题：
‏When a vector field satisfies (    ), it can be expressed by the gradient of a scalar field.‎
选项：
A:
B:
C:
D:
答案: 【 】

3、单选题：

​

‏选项：
A:
B:
C:
D:
答案: 【 】

2.1 Quiz (Electric Field Intensity of Electrostatic Field)

1、单选题：

‌

‏选项：
A:
B:
C:
D:
答案: 【 】

2、单选题：
‌A point charge q in vacuum is located at the coordinate origin. The electric field intensity at P (0, 2, 2) produced by the point charge is‎
选项：
A:
B:
C:
D:
答案: 【 】

3、单选题：

‍

‍选项：
A: It is proportional to r.
B: It is inversely proportional to r.
C:
D: It is independent of r.
答案: 【 】

4、单选题：
‏The radius of a uniformly charged conducting sphere is R and the charge quantity is Q. The electric field intensity inside the conductor is‍
选项：
A: 0
B:
C:
D:
答案: 【 0】

2.10 Quiz(The Method of Electric Axes)

1、单选题：

‏

‌选项：
A: The method of electric axes is applicable for the region inside and outside the conducting cylinders.
B:
C:
D: The essence of the method of electric axes is to replace the induced charge distribution on the conductor surfaces with the imaginary concentrated line charges outside the field boundary.
答案: 【 The essence of the method of electric axes is to replace the induced charge distribution on the conductor surfaces with the imaginary concentrated line charges outside the field boundary.】

2、单选题：

‎

‍选项：
A:
B:
C:
D:
答案: 【 】

3、判断题：
‏We can use the Gauss’s law and superposition principle to calculate the electric field of two parallel infinite line charges. ‍
选项：
A: 正确
B: 错误
答案: 【 正确】

4、判断题：

‏

‎选项：
A: 正确
B: 错误
答案: 【 错误】

5、判断题：
‏The introduction of imaginary concentrated line charges must keep the original boundary conditions unchanged.‎
选项：
A: 正确
B: 错误
答案: 【 正确】

6、判断题：
‍The theoretical basis of the method of electric axes is the uniqueness theorem.‍
选项：
A: 正确
B: 错误
答案: 【 正确】

7、判断题：
‌The method of electric axes can be used to solve the external electric field of two long parallel charged conducting cylinders with different radii.‎
选项：
A: 正确
B: 错误
答案: 【 正确】

2.11 Quiz(Capacitance)

1、单选题：
​The capacitance of a capacitor is related to‏
选项：
A: the voltage of the capacitor
B: the charge of the capacitor
C: the shape and dielectric of the capacitor
D: the electric field intensity of the capacitor
答案: 【 the shape and dielectric of the capacitor】

2、单选题：
About capacitance, which is false?‍
选项：
A: Capacitance is the ratio of the magnitude of the charge on either conductor to the magnitude of the potential difference between two conductors.
B: Capacitance is only related to the charge.
C: Capacitance is independent of the potential and total charge of the capacitor.
D: A capacitor is a device that stores electric energy, usually consisting of two conductors.
答案: 【 Capacitance is only related to the charge.】

3、单选题：