The most prominent study made by supernovae (SNe), cosmic microwave background (CMB), and baryonic acoustic oscillations (BAO) in modern cosmology is the accelerated expansion of the universe. Still, the universe holds the greatest mysteries of its evolution, such as the accelerated expansion's origin and cause. Many cosmologists take many modified theories that alternate with Einstein's theory into account to understand the accelerated expansion of the universe. Researchers are paying attention to these alternative theories because it is thought to offer a natural gravitational alternative to dark energy, which explains the universe's dark energy and late-time cosmic acceleration. Dark energy is highly considered the main element for accelerated expansion. Many studies have been executed for dark energy models in different gravitational theories in both the isotropic and anisotropic backgrounds. Cosmologists ^{ }^{ }^{ }^{ }^{ }^{ }^{ }^{ }^{ }^{ }^{ }

In cosmology, the magnetic field plays a crucial role in characterizing the ionized behavior that conducts energy fluctuations during the universe's expansion. The existence of the magnetic field affects the expansion independent of its strength and may result in anisotropy in the accelerated expansion (Matravers and Tsagas^{ }^{ }^{ }^{ }

The Bianchi type-III spacetime is studied abundantly because of the unique geometric characteristics that set it apart from the other Bianchi types. The present work is motivated by the studies on Bianchi type-III spacetime in various contexts. In this study, we try to firm the knowledge of the Bianchi universe, considering the scalar-tensor theory of gravitation in the presence of an electromagnetic field. In order to obtain the exact solutions of the field equation, the special form of time-dependent deceleration parameter generalized by Banerjee and Das^{ }

The metric for Bianchi type-III considered as

where A, B, and C are the function of cosmic time t only.

The field equation given by Sen and Dunn^{ }

where

The energy-momentum tensor with the presence of an electromagnetic field is

Here

From the Maxwell equation,

Eq. (5) leads to the result

where K and m are constants.

The field equation (2) with the equation (3), (4), and (6) for the equation (1) are

The average scale factor for Bianchi type-III spacetime is

The spatial volume, Hubble parameter is defined as

And deceleration parameter is defined as

The expansion scalar, shear scalar, and the anisotropic parameter are

where,

From equation (11), by considering m = 1, we have

Where n is the integration constant. Here we consider

Here, the nonlinear equation (20), (21), and (22) contains the unknown variables

To obtain the model compatible with the cosmological observation, we consider the variable deceleration parameter ^{15}) given by

where ^{ }^{ }^{ }^{ }

From equation (23), we obtain the Hubble parameter as

where

As Collins et al.^{ }

here,

We consider the gauge function for the model as

where,

From the equation (24) by integration, we have the scale factor as

Here,

Thus using equation (27) in equation (12), we get the following result as

The model (1) with the equation (28) and (29) reduces to

From the equation (20)-(22), we obtain the following energy density and pressure using equations (26), (28), and (29)

The spatial volume, expansion scalar, shear scalar, and anisotropic parameter for the model are as follows

Thus we also have

Energy condition and Statefinder parameter

From the following result, the energy condition identified that the Null Energy Condition (NEC), the Weak Energy Condition (WEC), and the Strong Energy Condition (SEC) are satisfied throughout the cosmic evolution of the model. The model's Dominant Energy Condition (DEC)l rapidly increases from negative phase to positive boundary after some cosmic time

The statefinder parameter {r,s} introduced by Shani et al.^{ }

Here, H is the Hubble parameter, and q is the deceleration parameter. The cosmological diagnostic pair {r,s} allow us to determine the characteristic properties of the dark energy in a model-independent approach. With the equations (23) and (24), we can rewrite the diagnostic pair {r,s} as

We observe from the above result that when

The equation (30) represents the model for the Bianchi type-III cosmological model with the electromagnetic field in the framework of Sen-Dunn scalar-tensor theory. The physical and geometrical parameters for the model are discussed above:

• The plotting of the figures are drawn against time (Gyr) by considering the values

• The model is expanding, shearing, and non-rotating, with the spatial volume increasing from the finite volume at

• The relation ^{ }^{23.}

• The model's energy density and the pressure given by equation (31) and (32)positively decreases.Also, it tends to be zero as ^{ }^{ }^{4)}.

• Initially, the dominant energy condition (DEC) gets violated for time

• From the above result (43) and (44), the nature of the statefinder parameter is obtained as_{0} in the framework of Sen-Dunn theory (Basumatary and Dewri^{ }^{24).}

This paper investigates the solutions of Bianchi type-III spacetime in the presence of an electromagnetic field in the Sen-Dunn scalar-tensor theory of gravitation. To deliver the solutions to the field equations, we consider the time-dependent deceleration parameter q, a signature flip property (Banerjee and Das^{ }^{ }