(A): In equation `F=q(E+v xx B)` when v = 0, any force on the charge must arise from the electric field term E alone
(R): To explain, the existence of induced emf or induced current in static conductor kept in time - varying magnetic field, we must assume that a time - varying magnetic field generates an electric field

Options

A. Both A and R are true and R is the correct explanation
B. Both A and R are true but R is not the correct explanation of A
C. A is true but R is false
D. Both A and R are false

Answer

To solve the question, we will analyze both statements (A) and (R) separately and determine their validity.

### Step-by-Step Solution:

**Step 1: Analyze Statement (A)**
The equation given is \( F = q(E + v \times B) \). Here, \( F \) is the force on a charge \( q \), \( E \) is the electric field, \( v \) is the velocity of the charge, and \( B \) is the magnetic field. When \( v = 0 \), the term \( v \times B \) becomes zero. Therefore, the force \( F \) simplifies to \( F = qE \). This means that if the charge is at rest, any force acting on it must arise solely from the electric field \( E \). Thus, Statement (A) is **true**.

**Step 2: Analyze Statement (R)**
Statement (R) discusses the existence of induced EMF (Electromotive Force) or induced current in a static conductor placed in a time-varying magnetic field. According to Faraday's law of electromagnetic induction, the induced EMF in a closed loop is given by:
\[ \mathcal{E} = -\frac{d\Phi_B}{dt} \]
where \( \Phi_B \) is the magnetic flux. A time-varying magnetic field generates an electric field, which can induce an EMF in a conductor. This is also supported by Maxwell's equations, specifically that the curl of the electric field \( \nabla \times E \) is equal to the negative rate of change of the magnetic field \( -\frac{\partial B}{\partial t} \). Therefore, Statement (R) is also **true**.

**Step 3: Determine the relationship between (A) and (R)**
Both statements (A) and (R) are true, but (R) serves to explain a different concept related to induced EMF in a time-varying magnetic field. Therefore, while both are true, (R) does not directly explain (A).

### Conclusion:
- Statement (A) is true.
- Statement (R) is true but does not directly explain (A).

Thus, the answer to the question is that both statements are true, but (R) does not explain (A).